Units and Measurements

200 questions · Physics · JEE Main

Units and Measurements

200 questions · Physics · JEE Main

Match List I with List II. Choose the correct answer from the options given below: Includes table2025 · 2 Apr · Shift 1 · Q58 · MCQ
If $μ_{0}$ and $ϵ_{0}$ are the permeability and permittivity of free space, respectively, then the dimension of $(\frac{1}{μ _{0} ϵ _{0}})$ is :2025 · 2 Apr · Shift 2 · Q54 · MCQ
Given a charge q , current I and permeability of vacuum $μ_{o^{*}}$ . Which of the following quantity has the dimension of momentum ?2025 · 2 Apr · Shift 2 · Q69 · MCQ
A person measures mass of 3 different particles as $435.42 g, 226.3 g$ and 0.125 g . According to the rules for arithmetic operations with significant figures, the addition of the masses of 3 particles will be.2025 · 3 Apr · Shift 1 · Q52 · MCQ
$Match the LIST-I with LIST-II$ Choose the correct answer from the options given below: Includes table2025 · 3 Apr · Shift 2 · Q64 · MCQ
A physical quantity C is related to four other quantities $p, q, r$ and s as follows $C = \frac{p q ^{2}}{r ^{3} s}$ The percentage errors in the measurement of $p, q, r$ and s are $1%, 2%, 3%$ …2025 · 3 Apr · Shift 2 · Q75 · Numerical
In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $M^{P} L^{Q} T^{R} A^{S}$ , where value of ' $Q$ ' and ' $R$ ' are2025 · 4 Apr · Shift 1 · Q52 · MCQ
In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of $[M^{P} L^{Q} T^{R} A^{S}]$ . The value of P…2025 · 4 Apr · Shift 2 · Q56 · MCQ
For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains 300 equal divisions equals to 15 cm . The vernier scale attached to the microscope has 25 divisions equals to 24 divisions…2025 · 4 Apr · Shift 2 · Q61 · MCQ
The dimension of $\frac{μ _{0}}{ϵ _{0}}$ is equal to that of: ( $μ_{0}$ = Vacuum permeability and $ϵ_{0}$ = Vacuum permittivity)2025 · 7 Apr · Shift 2 · Q51 · MCQ
Match List - I with List - II. Choose the correct answer from the options given below : Includes table2025 · 7 Apr · Shift 2 · Q56 · MCQ
A quantity Q is formulated as $X^{- 2} Y^{+ \frac{3}{2}} Z^{- \frac{2}{5}}$ . X, Y, and Z are independent parameters which have fractional errors of 0.1, 0.2, and 0.5, respectively in measurement. The maximum fractional error of Q is2025 · 8 Apr · Shift 2 · Q54 · MCQ
If $B$ is magnetic field and $μ_{0}$ is permeability of free space, then the dimensions of $(B / μ_{0})$ is2025 · 22 Jan · Shift 1 · Q51 · MCQ
Given below are two statements : Statement I: In a vernier callipers, one vernier scale division is always smaller than one main scale division. Statement II : The vernier constant is given by one main scale division multiplied by the…2025 · 22 Jan · Shift 1 · Q63 · MCQ
The maximum percentage error in the measurment of density of a wire is [Given, mass of wire $= (0.60 \pm 0.003) g$ radius of wire $= (0.50 \pm 0.01) cm$ length of wire $= (10.00 \pm 0.05) cm]$ 2025 · 22 Jan · Shift 2 · Q55 · MCQ
The position of a particle moving on $x$ -axis is given by $x (t) = A sin t + B cos^{2} t + C t^{2} + D$ , where $t$ is time. The dimension of $\frac{A B C}{D}$ is2025 · 23 Jan · Shift 1 · Q55 · MCQ
The energy of a system is given as $E (t) = α^{3} e^{- β t}$ , where t is the time and $β = 0.3 s^{- 1}$ . The errors in the measurement of $α$ and $t$ are $1.2%$ and $1.6%$ , respectively. At…2025 · 23 Jan · Shift 2 · Q66 · MCQ
Match List - I with List - II Choose the correct answer from the options given below : Includes table2025 · 23 Jan · Shift 2 · Q67 · MCQ
For an experimental expression $y = \frac{32.3 \times 1125}{27.4}$ , where all the digits are significant. Then to report the value of $y$ we should write2025 · 24 Jan · Shift 1 · Q70 · MCQ
The least count of a screw guage is 0.01 mm . If the pitch is increased by $75%$ and number of divisions on the circular scale is reduced by $50%$ , the new least count will be $\times 1 0^{- 3} mm$ 2025 · 24 Jan · Shift 1 · Q73 · Numerical
A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm , respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the…2025 · 28 Jan · Shift 1 · Q74 · Numerical
Match List - I with List - II. Choose the correct answer from the options given below: Includes table2025 · 28 Jan · Shift 2 · Q64 · MCQ
The pair of physical quantities not having the same dimensions is :2025 · 29 Jan · Shift 1 · Q54 · MCQ
The expression given below shows the variation of velocity (v) with time (t), $v = At^{2} + \frac{Bt}{C + t}$ . The dimension of ABC is :2025 · 29 Jan · Shift 1 · Q55 · MCQ
Match List - I with List - II. Choose the correct answer from the options given below : Includes table2025 · 29 Jan · Shift 2 · Q61 · MCQ
$A physical quantity Q is related to four observables a, b, c, d as follows : Q = \frac{a b ^{4}}{c d}$ where, $a = (60 \pm 3) Pa; b = (20 \pm 0.1) m; c = (40 \pm 0.2) Nsm^{- 2}$ …2025 · 29 Jan · Shift 2 · Q71 · Numerical
10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is :2024 · 1 Feb · Shift 1 · Q63 · MCQ
The dimensional formula of angular impulse is :2024 · 1 Feb · Shift 1 · Q65 · MCQ
The radius $(r)$ , length $(l)$ and resistance $(R)$ of a metal wire was measured in the laboratory as $r = (0.35 \pm 0.05) cm R = (100 \pm 10) ohm l = (15 \pm 0.2) cm$ …2024 · 1 Feb · Shift 1 · Q73 · MCQ
Match List - I with List - II. Choose the correct answer from the options given below : Includes table2024 · 1 Feb · Shift 2 · Q66 · MCQ
The equation of stationary wave is : $y = 2 a sin (\frac{2 π nt}{λ}) cos (\frac{2 π x}{λ}) .$ Which of the following is NOT correct :2024 · 4 Apr · Shift 1 · Q72 · MCQ
Applying the principle of homogeneity of dimensions, determine which one is correct, where $T$ is time period, $G$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.2024 · 4 Apr · Shift 2 · Q61 · MCQ
Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as $4.62 s, 4.632 s, 4.6 s$ and $4.64 s$ . The arithmetic mean of these readings…2024 · 5 Apr · Shift 1 · Q77 · MCQ
What is the dimensional formula of $a b^{- 1}$ in the equation $(P + \frac{a}{V ^{2}}) (V - b) = RT$ , where letters have their usual meaning.2024 · 5 Apr · Shift 2 · Q62 · MCQ
A vernier callipers has 20 divisions on the vernier scale, which coincides with $1 9^{th}$ division on the main scale. The least count of the instrument is $0.1 mm$ . One main scale division is equal to …2024 · 5 Apr · Shift 2 · Q73 · MCQ
To find the spring constant $(k)$ of a spring experimentally, a student commits $2%$ positive error in the measurement of time and $1%$ negative error in measurement of mass. The percentage error in determining value of $k$ is :2024 · 6 Apr · Shift 1 · Q65 · MCQ
Match List I with List II Choose the correct answer from the options given below: Includes table2024 · 6 Apr · Shift 1 · Q69 · MCQ
While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is $1 mm$ and circular scale reading is equal to 42 divisions. Pitch of screw gauge is $1 mm$ and it has 100…2024 · 6 Apr · Shift 1 · Q73 · MCQ
In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $4^{th}$ division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49…2024 · 6 Apr · Shift 2 · Q66 · MCQ
In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division $= 49 MSD; 20$ divisions on main scale in each $cm$ For mark on paper $MSR = 8.45 cm, VC = 26$ …2024 · 6 Apr · Shift 2 · Q78 · MCQ
In an expression $a \times 1 0^{b}$ :2024 · 8 Apr · Shift 1 · Q65 · MCQ
The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to $1 mm$ . The main scale reading is $2 cm$ …2024 · 8 Apr · Shift 1 · Q74 · MCQ
If $ϵ_{o}$ is the permittivity of free space and $E$ is the electric field, then $ϵ_{o} E^{2}$ has the dimensions :2024 · 8 Apr · Shift 2 · Q64 · MCQ
There are 100 divisions on the circular scale of a screw gauge of pitch $1 mm$ . With no measuring quantity in between the jaws, the zero of the circular scale lies 5 divisions below the reference line. The diameter of a wire is…2024 · 8 Apr · Shift 2 · Q70 · MCQ
Least count of a vernier caliper is $\frac{1}{20 N} cm$ . The value of one division on the main scale is $1 mm$ . Then the number of divisions of main scale that coincide with $N$ divisions of vernier…2024 · 8 Apr · Shift 2 · Q72 · MCQ
The dimensional formula of latent heat is :2024 · 9 Apr · Shift 1 · Q63 · MCQ
One main scale division of a vernier caliper is equal to $m$ units. If $n^{th}$ division of main scale coincides with $(n + 1)^{th}$ division of vernier scale, the least count of the vernier caliper is :2024 · 9 Apr · Shift 1 · Q73 · MCQ
The de-Broglie wavelength associated with a particle of mass $m$ and energy $E$ is $h / 2 m E$ . The dimensional formula for Planck's constant is :2024 · 9 Apr · Shift 2 · Q77 · MCQ
Given below are two statements : Statement (I) : Planck's constant and angular momentum have same dimensions. Statement (II) : Linear momentum and moment of force have same dimensions. In the light of the above statements, choose the…2024 · 27 Jan · Shift 1 · Q77 · MCQ
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more…2024 · 27 Jan · Shift 2 · Q61 · MCQ
The resistance $R = \frac{V}{I}$ where $V = (200 \pm 5) V$ and $I = (20 \pm 0.2) A$ , the percentage error in the measurement of $R$ is :2024 · 29 Jan · Shift 1 · Q61 · MCQ
A physical quantity $Q$ is found to depend on quantities $a, b, c$ by the relation $Q = \frac{a ^{4} b ^{3}}{c ^{2}}$ . The percentage error in $a, b$ and $c$ are $3%, 4%$ and $5%$ respectively. Then, the percentage error in $Q$ is :2024 · 29 Jan · Shift 2 · Q63 · MCQ
Match List I with List II. Choose the correct answer from the options given below : Includes table2024 · 30 Jan · Shift 1 · Q72 · MCQ
If 50 Vernier divisions are equal to 49 main scale divisions of a traveling microscope and one smallest reading of main scale is $0.5 mm$ , the Vernier constant of traveling microscope is2024 · 30 Jan · Shift 2 · Q61 · MCQ
If mass is written as $m = k c^{P} G^{- 1/2} h^{1/2}$ then the value of $P$ will be : (Constants have their usual meaning with $k a$ dimensionless constant)2024 · 30 Jan · Shift 2 · Q79 · MCQ
If the percentage errors in measuring the length and the diameter of a wire are $0.1%$ each. The percentage error in measuring its resistance will be:2024 · 31 Jan · Shift 1 · Q76 · MCQ
A force is represented by $F = a x^{2} + b t^{\frac{1}{2}}$ where $x =$ distance and $t =$ time. The dimensions of $b^{2} / a$ are:2024 · 31 Jan · Shift 1 · Q78 · MCQ
Consider two physical quantities $A$ and $B$ related to each other as $E = \frac{B - x ^{2}}{A t}$ where $E, x$ and $t$ have dimensions of energy, length and time respectively. The dimension of $A B$ is2024 · 31 Jan · Shift 2 · Q62 · MCQ
The measured value of the length of a simple pendulum is $20 cm$ with $2 mm$ accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the…2024 · 31 Jan · Shift 2 · Q73 · MCQ
If the velocity of light $c$ , universal gravitational constant $G$ and Planck's constant $h$ are chosen as fundamental quantities. The dimensions of mass in the new system is :2023 · 1 Feb · Shift 2 · Q54 · MCQ
Two resistances are given as $R_{1} = (10 \pm 0.5) Ω$ and $R_{2} = (15 \pm 0.5) Ω$ . The percentage error in the measurement of equivalent resistance when they are connected in parallel is -2023 · 6 Apr · Shift 1 · Q56 · MCQ
Dimension of $\frac{1}{μ _{0} \in _{0}}$ should be equal to2023 · 8 Apr · Shift 1 · Q52 · MCQ
A cylindrical wire of mass $(0.4 \pm 0.01) g$ has length $(8 \pm 0.04) cm$ and radius $(6 \pm 0.03) mm$ . The maximum error in its density will be:2023 · 8 Apr · Shift 1 · Q58 · MCQ
Match List I with List II Choose the correct answer from the options given below: Includes table2023 · 8 Apr · Shift 2 · Q57 · MCQ
A physical quantity P is given as $P = \frac{a ^{2} b ^{3}}{c d}$ The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4% respectively. The percentage error in the measurement of quantity P will be2023 · 10 Apr · Shift 1 · Q48 · MCQ
In an experiment with vernier callipers of least count $0.1 mm$ , when two jaws are joined together the zero of vernier scale lies right to the zero of the main scale and 6th division of vernier scale coincides with the main scale…2023 · 10 Apr · Shift 2 · Q55 · MCQ
Given below are two statements : Statements I : Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances. Statements II : $$\mathrm{Au} In the light of the above statements, choose the most…2023 · 11 Apr · Shift 1 · Q49 · MCQ
If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be :2023 · 11 Apr · Shift 2 · Q58 · MCQ
Match List I with List II Choose the correct answer from the options given below: Includes table2023 · 12 Apr · Shift 1 · Q46 · MCQ
A body of mass $(5 \pm 0.5) kg$ is moving with a velocity of $(20 \pm 0.4) m / s$ . Its kinetic energy will be2023 · 13 Apr · Shift 1 · Q61 · MCQ
In the equation $[X + \frac{a}{Y ^{2}}] [Y - b] = R T, X$ is pressure, $Y$ is volume, $R$ is universal gas constant and $T$ is temperature. The physical quantity equivalent to the ratio $\frac{a}{b}$ is:2023 · 13 Apr · Shift 2 · Q46 · MCQ
The speed of a wave produced in water is given by $v = λ^{a} g^{b} ρ^{c}$ . Where $λ, g$ and $ρ$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $a, b$ and $c$ …2023 · 15 Apr · Shift 1 · Q56 · MCQ
Match List I with List II Choose the correct answer from the options given below : Includes table2023 · 24 Jan · Shift 1 · Q60 · MCQ
Match List I with List II Choose the correct answer from the options given below : Includes table2023 · 25 Jan · Shift 2 · Q59 · MCQ
Match List I with List II : Choose the correct answer from the options given below: Includes table2023 · 29 Jan · Shift 1 · Q57 · MCQ
The equation of a circle is given by $x^{2} + y^{2} = a^{2}$ , where a is the radius. If the equation is modified to change the origin other than (0, 0), then find out the correct dimensions of A and B in a new equation : $(x - A t)^{2} + (y - \frac{t}{B})^{2} = a^{2}$ …2023 · 29 Jan · Shift 2 · Q47 · MCQ
In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by $0.5 mm$ on a complete rotation of the circular scale. The zero of circular scale lies 6 divisions below the line of graduation when two…2023 · 30 Jan · Shift 1 · Q66 · Numerical
Match List I with List II: Choose the correct answer from the options given below: Includes table2023 · 30 Jan · Shift 2 · Q46 · MCQ
Match List I with List II Choose the correct answer from the options given below: Includes table2023 · 31 Jan · Shift 2 · Q58 · MCQ
Identify the pair of physical quantities which have different dimensions:2022 · 24 Jun · Shift 1 · Q47 · MCQ
Identify the pair of physical quantities that have same dimensions:2022 · 24 Jun · Shift 2 · Q46 · MCQ
If momentum [P], area $[A]$ and time $[T]$ are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is :2022 · 25 Jul · Shift 1 · Q41 · MCQ
The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are $1%, 2%$ and $3%$ respectively. The maximum percentage error in the detection of the dissipated heat will be :2022 · 25 Jul · Shift 2 · Q61 · MCQ
If $Z = \frac{A ^{2} B ^{3}}{C ^{4}}$ , then the relative error in Z will be :2022 · 25 Jun · Shift 1 · Q44 · MCQ
For $z = a^{2} x^{3} y^{\frac{1}{2}}$ , where 'a' is a constant. If percentage error in measurement of 'x' and 'y' are 4% and 12% respectively, then the percentage error for 'z' will be %.2022 · 25 Jun · Shift 2 · Q64 · Numerical
A screw gauge of pitch $0.5 mm$ is used to measure the diameter of uniform wire of length $6.8 cm$ , the main scale reading is $1.5 mm$ and circular scale reading is 7 . The calculated curved surface area of…2022 · 26 Jul · Shift 1 · Q63 · MCQ
In a Vernier Calipers, 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and $4^{th}$ …2022 · 26 Jul · Shift 2 · Q41 · MCQ
An expression for a dimensionless quantity P is given by $P = \frac{α}{β} lo g_{e} (\frac{k t}{β x})$ ; where $α$ and $β$ are constants, x is distance; k is Boltzmann constant and t is the…2022 · 26 Jun · Shift 1 · Q42 · MCQ
In a vernier callipers, each cm on the main scale is divided into 20 equal parts. If tenth vernier scale division coincides with nineth main scale division. Then the value of vernier constant will be $\times$ 10 $-$ …2022 · 26 Jun · Shift 1 · Q65 · Numerical
The dimension of mutual inductance is :2022 · 26 Jun · Shift 2 · Q47 · MCQ
A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on main scale and 50 Vernier scale divisions are equal to 49 main scale divisions, then least count of the travelling…2022 · 26 Jun · Shift 2 · Q71 · Numerical
A torque meter is calibrated to reference standards of mass, length and time each with $5%$ accuracy. After calibration, the measured torque with this torque meter will have net accuracy of :2022 · 27 Jul · Shift 1 · Q47 · MCQ
The one division of main scale of Vernier callipers reads $1 mm$ and 10 divisions of Vernier scale is equal to the 9 divisions on main scale. When the two jaws of the instrument touch each other, the zero of the Vernier lies to…2022 · 27 Jul · Shift 1 · Q64 · Numerical
An expression of energy density is given by $u = \frac{α}{β} sin (\frac{α x}{k t})$ , where $α, β$ are constants, $x$ is displacement, $k$ is Boltzmann constant and t is the temperature. The dimensions of $β$ …2022 · 27 Jul · Shift 2 · Q41 · MCQ
A silver wire has a mass (0.6 $\pm$ 0.006) g, radius (0.5 $\pm$ 0.005) mm and length (4 $\pm$ 0.04) cm. The maximum percentage error in the measurement of its density will be :2022 · 27 Jun · Shift 1 · Q44 · MCQ
The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be :2022 · 27 Jun · Shift 2 · Q45 · MCQ
The dimensions of $(\frac{B ^{2}}{μ _{0}})$ will be : (if $μ_{0}$ : permeability of free space and $B$ : magnetic field)2022 · 28 Jul · Shift 1 · Q47 · MCQ
Consider the efficiency of carnot's engine is given by $η = \frac{α β}{s i n θ} lo g_{e} \frac{β x}{k T}$ , where $α$ and $β$ are constants. If T is temperature, k is Boltzmann constant, $θ$ is angular…2022 · 28 Jul · Shift 2 · Q40 · MCQ
In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of $0.5 s$ is measured from time of 100 oscillation with a watch of $1 s$ resolution. If measured value of length is $10 cm$ …2022 · 28 Jul · Shift 2 · Q66 · Numerical
Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as $v_{2} = \frac{n}{m ^{2}} v_{1}$ and $a_{2} = \frac{a _{1}}{mn}$ respectively. Here m and n are constants. The relations for distance and time in two…2022 · 28 Jun · Shift 2 · Q50 · MCQ
A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22 mm, 1.23 mm, 1.19 mm and 1.20 mm. The percentage error is $\frac{x}{121} %$ . The value of x is .2022 · 28 Jun · Shift 2 · Q68 · Numerical
Given below are two statements : One is labelled as Assertion (A) and other is labelled as Reason (R). Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is $ρ$ and…2022 · 29 Jul · Shift 1 · Q48 · MCQ
A travelling microscope has 20 divisions per $cm$ on the main scale while its vernier scale has total 50 divisions and 25 vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling…2022 · 29 Jul · Shift 1 · Q65 · MCQ
In an experiment to find out the diameter of wire using screw gauge, the following observations were noted : (A) Screw moves $0.5 mm$ on main scale in one complete rotation (B) Total divisions on circular scale $= 50$ (C) Main… Includes diagram2022 · 29 Jul · Shift 1 · Q66 · MCQ
Match List I with List II. Choose the correct answer from the options given below : Includes table2022 · 29 Jul · Shift 2 · Q45 · MCQ
The Vernier constant of Vernier callipers is 0.1 mm and it has zero error of ( $-$ 0.05) cm. While measuring diameter of a sphere, the main scale reading is 1.7 cm and coinciding vernier division is 5. The corrected diameter will be $\times$ …2022 · 29 Jun · Shift 2 · Q62 · Numerical
If n main scale divisions coincide with (n + 1) vernier scale divisions. The least count of vernier callipers, when each centimetre on the main scale is divided into five equal parts, will be :2022 · 30 Jun · Shift 1 · Q43 · MCQ
A student determined Young's Modulus of elasticity using the formula $Y = \frac{M g L ^{3}}{4 b d ^{3} δ}$ . The value of g is taken to be 9.8 m/s2, without any significant error, his observation are as following. Then the fractional… Includes table2021 · 1 Sep · Shift 2 · Q54 · MCQ
One main scale division of a vernier callipers is 'a' cm and nth division of the vernier scale coincide with (n $-$ 1)th division of the main scale. The least count of the callipers in mm is :2021 · 16 Mar · Shift 1 · Q59 · MCQ
The resistance R = $\frac{V}{I}$ , where V = (50 $\pm$ 2)V and I = (20 $\pm$ 0.2)A. The percentage error in R is 'x'%. The value of 'x' to the nearest integer is .2021 · 16 Mar · Shift 1 · Q66 · Numerical
In order to determine the Young's Modulus of a wire of radius 0.2 cm (measured using a scale of least count = 0.001 cm) and length 1m (measured using a scale of least count = 1 mm), a weight of mass 1 kg (measured using a scale of least…2021 · 16 Mar · Shift 2 · Q56 · MCQ
The vernier scale used for measurement has a positive zero error of 0.2 mm. If while taking a measurement it was noted that '0' on the vernier scale lies between 8.5 cm and 8.6 cm, vernier coincidence is 6, then the correct value of…2021 · 17 Mar · Shift 1 · Q57 · MCQ
The radius of a sphere is measured to be (7.50 $\pm$ 0.85) cm. Suppose the percentage error in its volume is x. The value of x, to the nearest x, is .2021 · 18 Mar · Shift 2 · Q66 · Numerical
If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units. Then the dimension of mass (m) in terms of t, v and l is :2021 · 20 Jul · Shift 2 · Q57 · MCQ
Three students S1, S2 and S3 perform an experiment for determining the acceleration due to gravity (g) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations… Includes table2021 · 22 Jul · Shift 2 · Q66 · Numerical
The work done by a gas molecule in an isolated system is given by, $W = α β^{2} e^{- \frac{x ^{2}}{α k T}}$ , where x is the displacement, k is the Boltzmann constant and T is the temperature. $α$ and $β$ are…2021 · 24 Feb · Shift 1 · Q59 · MCQ
Match List - I with List - II : Choose the correct answer from the options given below : Includes table2021 · 25 Feb · Shift 1 · Q51 · MCQ
The pitch of the screw gauge is 1 mm and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies 8 divisions below the reference line. When a wire is placed between the…2021 · 25 Feb · Shift 1 · Q56 · MCQ
If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity $\frac{1}{4 π ε _{0}} \frac{∣ e ∣ ^{2}}{h c}$ has dimensions of :2021 · 25 Feb · Shift 2 · Q63 · MCQ
Student A and student B used two screw gauges of equal pitch and 100 equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is 0.322 cm. The absolute value of the difference between the… Includes diagram2021 · 25 Jul · Shift 1 · Q63 · Numerical
The force is given in terms of time t and displacement x by the equation F = A cos Bx + C sin Dt The dimensional formula of $\frac{A D}{B}$ is :2021 · 25 Jul · Shift 2 · Q58 · MCQ
In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by 0.5 mm on a complete rotation. For a particular…2021 · 26 Aug · Shift 1 · Q57 · MCQ
If E, L, M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula P = EL2M $-$ 5G $-$ 2 are :2021 · 26 Aug · Shift 1 · Q60 · MCQ
Match List - I with List - II Choose the most appropriate answer from the options given below : Includes diagram2021 · 26 Aug · Shift 2 · Q59 · MCQ
If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is :2021 · 26 Aug · Shift 2 · Q61 · MCQ
The acceleration due to gravity is found upto an accuracy of 4% on a planet. The energy supplied to a simple pendulum to known mass 'm' to undertake oscillations of time period T is being estimated. If time period is measured to an…2021 · 26 Aug · Shift 2 · Q66 · Numerical
In a typical combustion engine the workdone by a gas molecule is given by $W = α^{2} β e^{\frac{- β x ^{2}}{k T}}$ , where x is the displacement, k is the Boltzmann constant and T is the temperature. If $α$ and $β$ …2021 · 26 Feb · Shift 1 · Q52 · MCQ
If 'C' and 'V' represent capacity and voltage respectively then what are the dimensions of $λ$ where C/V = $λ$ ?2021 · 26 Feb · Shift 2 · Q53 · MCQ
Which of the following is not a dimensionless quantity?2021 · 27 Aug · Shift 1 · Q42 · MCQ
If E and H represents the intensity of electric field and magnetising field respectively, then the unit of E/H will be :2021 · 27 Aug · Shift 1 · Q43 · MCQ
Match List - I with List - II. Choose the most appropriate answer from the options given below : Includes table2021 · 27 Aug · Shift 2 · Q52 · MCQ
If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density :2021 · 27 Aug · Shift 2 · Q53 · MCQ
Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5 mm and there are 50 total divisions on circular scale, then least count is 0.001 cm. Reason R : Least Count = $\frac{P i t c h}{T o t a l d i v i s i o n s o n c i r c u l a r sc a l e}$ …2021 · 27 Jul · Shift 1 · Q65 · MCQ
A physical quantity 'y' is represented by the formula $y = m^{2} r^{- 4} g^{x} l^{- \frac{3}{2}}$ If the percentage errors found in y, m, r, l and g are 18, 1, 0.5, 4 and p respectively, then find the value of x and p.2021 · 27 Jul · Shift 2 · Q58 · MCQ
Match List - I with List - II. Choose the most appropriate answer from the option given below : Includes table2021 · 31 Aug · Shift 1 · Q57 · MCQ
Which of the following equations is dimensionally incorrect? Where t = time, h = height, s = surface tension, $θ$ = angle, $ρ$ = density, a, r = radius, g = acceleration due to gravity, v = volume, p = pressure, W = work done, T =…2021 · 31 Aug · Shift 1 · Q59 · MCQ
If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be :2021 · 31 Aug · Shift 2 · Q53 · MCQ
The diameter of a spherical bob is measured using a vernier callipers. 9 divisions of the main scale, in the vernier callipers, are equal to 10 divisions of vernier scale. One main scale division is 1 mm. The main scale reading is 10 mm…2021 · 31 Aug · Shift 2 · Q67 · Numerical
The least count of the main scale of a vernier callipers is 1 mm. Its vernier scale is divided into 10 divisions and coincide with 9 divisions of the main scale. When jaws are touching each other, the 7th division of vernier scale…2020 · 2 Sep · Shift 1 · Q38 · MCQ
If speed V, area A and force F are chosen as fundamental units, then the dimension of Young’s modulus will be2020 · 2 Sep · Shift 1 · Q46 · MCQ
If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is2020 · 2 Sep · Shift 2 · Q55 · MCQ
Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as2020 · 3 Sep · Shift 1 · Q65 · MCQ
Amount of solar energy received on the earth’s surface per unit area per unit time is defined a solar constant. Dimension of solar constant is :2020 · 3 Sep · Shift 2 · Q53 · MCQ
Dimensional formula for thermal conductivity is (here K denotes the temperature):2020 · 4 Sep · Shift 1 · Q44 · MCQ
A quantity x is given by $(\frac{I F v ^{2}}{W L ^{4}})$ in terms of moment of inertia I, force F, velocity v, work W and Length L. The dimensional formula for x is same as that of :2020 · 4 Sep · Shift 2 · Q49 · MCQ
A physical quantity z depends on four observables a, b, c and d, as z = $\frac{a ^{2} b ^{\frac{2}{3}}}{c d ^{3}}$ . The percentages of error in the measurement of a, b, c and d are 2%, 1.5%, 4% and 2.5% respectively. The percentage…2020 · 5 Sep · Shift 1 · Q45 · MCQ
The quantities x = $\frac{1}{μ _{0} ε _{0}}$ , y = $\frac{E}{B}$ and z = $\frac{l}{C R}$ are defined where C-capacitance, R-Resistance, l-length, E-Electric field, B-magnetic field and $ε_{0}$ , ${{\mu…2020 · 5 Sep · Shift 2 · Q51 · MCQ
A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of 0.5mm is noticed on the pitch scale.…2020 · 6 Sep · Shift 1 · Q56 · MCQ
The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is $(\frac{x}{100})$ %. If the relative errors in measuring the mass and the…2020 · 6 Sep · Shift 1 · Q60 · Numerical
A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings 5.50 mm, 5.55 mm, 5.45 mm, 5.65 mm. The average of these four readings is 5.5375 mm and the…2020 · 6 Sep · Shift 2 · Q57 · MCQ
The dimension of $\frac{B ^{2}}{2 μ _{0}}$ , where B is magnetic field and $μ_{0}$ is the magnetic permeability of vacuum, is :2020 · 7 Jan · Shift 2 · Q44 · MCQ
The dimension of stopping potential V0 in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and Gravitational constant 'G' and ampere A is :2020 · 8 Jan · Shift 1 · Q44 · MCQ
If the screw on a screw-gauge is given six rotations, it moves by 3 mm on the main scale. If there are 50 divisions on the circular scale the least count of the screw gauge is :2020 · 9 Jan · Shift 1 · Q56 · MCQ
A quantity f is given by $f = \frac{h c ^{5}}{G}$ where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of :2020 · 9 Jan · Shift 1 · Q67 · MCQ
For the four sets of three measured physical quantities as given below. Which of the following options is correct ? (i) A1 = 24.36, B1 = 0.0724, C1 = 256.2 (ii) A2 = 24.44, B2 = 16.082, C2 = 240.2 (iii) A3 = 25.2, B3 = 19.2812, C3 =…2020 · 9 Jan · Shift 2 · Q48 · MCQ
In SI units, the dimensions of $\frac{\in _{0}}{μ _{0}}$ is :2019 · 8 Apr · Shift 1 · Q52 · MCQ
In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be 30 s. The length of…2019 · 8 Apr · Shift 2 · Q52 · MCQ
If surface tension (S), Moment of inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be :-2019 · 8 Apr · Shift 2 · Q58 · MCQ
In the density measurement of a cube, the mass and edge length are measured as (10.00 ± 0.10) kg and (0.10 ± 0.01) m, respectively. The error in the measurement of density is :2019 · 9 Apr · Shift 1 · Q72 · MCQ
The area of a square is 5.29 cm2. The area of 7 such squares taking into account the significant figures is :-2019 · 9 Apr · Shift 2 · Q58 · MCQ
A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is :2019 · 9 Jan · Shift 1 · Q59 · MCQ
The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the…2019 · 9 Jan · Shift 2 · Q55 · MCQ
Expression for time in terms of G(universal gravitional constant), h (Planck constant) and c (speed of light) is proportional to :2019 · 9 Jan · Shift 2 · Q66 · MCQ
In the formula X = 5YZ2 , X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units?2019 · 10 Apr · Shift 2 · Q64 · MCQ
The density of a material in SI units is 128 kg m–3 . In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is -2019 · 10 Jan · Shift 1 · Q55 · MCQ
The diameter and height of a cylinder are measured by a meter scale to be 12.6 $\pm$ 0.1 cm and 34.2 $\pm$ 0.1 cm, respectively. What will be the value of its volume in appropriate significant figures ?2019 · 10 Jan · Shift 2 · Q69 · MCQ
The force of interaction between two atoms is given by F = $α β$ exp $(- \frac{x ^{2}}{α k t})$ ; where x is the distance, k is the Boltzmann constant and T is temperature and $α$ and $β$ are two…2019 · 11 Jan · Shift 1 · Q59 · MCQ
If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young,s modulus will be:2019 · 11 Jan · Shift 2 · Q53 · MCQ
Which of the following combinations has the dimension of electrical resistance ( $\in$ 0 is the permittivity of vacuum and $μ$ 0 is the permeability of vacuum)?2019 · 12 Apr · Shift 1 · Q56 · MCQ
The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 $μ$ m diameter of a wire is :2019 · 12 Jan · Shift 1 · Q48 · MCQ
Let $ℓ$ , r, C and V represent inductance, resistance, capacitance and voltage, respectively. The dimension of $\frac{ℓ}{r C V}$ in SI units will be :2019 · 12 Jan · Shift 2 · Q62 · MCQ
In a screw gauge, $5$ complete rotations of the screw cause it to move a linear distance of $0.25 c m .$ There are $100$ circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of $4$ main scale…2018 · 15 Apr · Shift 1 · Q54 · MCQ
The relative error in the determination of the surface area of sphere is $α$ . Then the relative error in the determination of its volume is :2018 · 15 Apr · Shift 1 · Q65 · MCQ
The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants G, h and c. Which of the following correctly gives…2018 · 15 Apr · Shift 2 · Q66 · MCQ
The relative uncertainly in the period of a satellite orbiting around the earth is 10-2. If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is :2018 · 16 Apr · Shift 1 · Q64 · MCQ
The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity A = $\frac{P ^{3} Q ^{2}}{R S} .$ The maximum percentage error in the value of A will be :2018 · 16 Apr · Shift 1 · Q69 · MCQ
The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the…2018 · Shift 0 · Q67 · MCQ
Time (T), velocity (C) and angular momentum (h) are chosen as fundamentalquantities instead of mass, length and time. In terms of these, the dimensions of mass would be :2017 · 8 Apr · Shift 1 · Q70 · MCQ
A physical quantity P is described by the relation P = a $^{\frac{1}{2}}$ b2 c3 d $-$ 4 If the relative errors in the measurement of a, b, c and d respectively, are 2%, 1%, 3% and 5%, then the relative error in P will be :2017 · 9 Apr · Shift 1 · Q66 · MCQ
The following observations were taken for determining surface tension T of water by capillary method: diameter of capillary, D = 1.25 $\times$ 10-2 m rise of water, h = 1.45 $\times$ 10-2m Using g = 9.80 m/s2 and the simplified relation T…2017 · Shift 0 · Q67 · MCQ
In the following ‘I’ refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity :2016 · 9 Apr · Shift 1 · Q66 · MCQ
A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD = C ln (BD) holds true. Then which of the combination is not a meaningful quantity ?2016 · 10 Apr · Shift 1 · Q60 · Multiple correct
A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought…2016 · Shift 0 · Q62 · MCQ
A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be :2016 · Shift 0 · Q63 · MCQ
A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?2014 · Shift 0 · Q74 · MCQ
Let [ $ε_{0}$ ] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then:2013 · Shift 0 · Q75 · MCQ
A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading: 58.5 degree Vernier scale reading : 09 divisions Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on…2012 · Shift 0 · Q68 · MCQ
Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in…2012 · Shift 0 · Q69 · MCQ
A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading : 0 mm Circular scale reading : 52 divisions Given that 1 mm on main scale corresponds to 100 divisions of the circular scale. The…2011 · Shift 0 · Q79 · MCQ
The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 $\times$ 10–3 are2010 · Shift 0 · Q78 · MCQ
In an experiment the angles are required to be measured using an instrument, 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a degree(= $0. 5^{\circ}$ …2009 · Shift 0 · Q76 · MCQ
An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distances are measured by2008 · Shift 0 · Q62 · MCQ
Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of − 0.03 mm while…2008 · Shift 0 · Q86 · MCQ
A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms−1. The magnitude of its momentum is recorded as2008 · Shift 0 · Q87 · MCQ
The dimension of magnetic field in M, L, T and C (coulomb) is given as2008 · Shift 0 · Q88 · MCQ
Out of the following pair, which one does NOT have identical dimensions is2005 · Shift 0 · Q168 · MCQ
Which one of the following represents the correct dimensions of the coefficient of viscosity?2004 · Shift 0 · Q183 · MCQ
Dimensions of $\frac{1}{μ _{0} ε _{0}}$ , where symbols have their usual meaning, are2003 · Shift 0 · Q170 · MCQ
The physical quantities not having same dimensions are2003 · Shift 0 · Q171 · MCQ
Identify the pair whose dimensions are equal2002 · Shift 0 · Q167 · MCQ