Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Properties of Matter question

2023 · 13 Apr · Shift 2 · Q48
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Properties of Matter
  5. /2023 · 13 Apr · Shift 2 · Q48

Properties of Matter question

2023 · 13 Apr · Shift 2 · Q48

JEE MainPhysicsProperties of MatterMCQ+4 / −1
Given below are two statements: one is labelled as Assertion A\mathbf{A}A and the other is labelled as Reason R\mathbf{R}R Assertion A : A spherical body of radius (5±0.1)mm(5 \pm 0.1) \mathrm{mm}(5±0.1)mm having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is 4%4 \%4%. Reason R : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius. In the light of the above statements, choose the correct answer from the options given below
  1. A
    A is false but R\mathbf{R}R is true
  2. B
    A\mathrm{A}A is true but R\mathbf{R}R is false
  3. C
    Both A\mathbf{A}A and R\mathbf{R}R are true but R\mathbf{R}R is NOT the correct explanation of A\mathbf{A}A
  4. D
    Both A\mathbf{A}A and R\mathbf{R}R are true and R\mathbf{R}R is the correct explanation of A\mathbf{A}A
View written solutionFree

Correct answer: B

  1. Use the formula for terminal velocity

For a small spherical body falling through a viscous liquid, Stokes' law gives

vt=29r2(ρ−σ)gηv_t = \frac{2}{9}\frac{r^2(\rho-\sigma)g}{\eta}vt​=92​ηr2(ρ−σ)g​

where:

  • rrr = radius of sphere
  • ρ\rhoρ = density of sphere
  • σ\sigmaσ = density of liquid
  • η\etaη = coefficient of viscosity

So,

vt∝r2v_t \propto r^2vt​∝r2

not inversely proportional to rrr.

Hence, Reason R is false.

  1. Check the assertion using error propagation

Since

vt∝r2v_t \propto r^2vt​∝r2

percentage error in terminal velocity is

Δvtvt×100=2Δrr×100\frac{\Delta v_t}{v_t} \times 100 = 2\frac{\Delta r}{r} \times 100vt​Δvt​​×100=2rΔr​×100

Given:

r=5±0.1 mmr = 5 \pm 0.1\ \text{mm}r=5±0.1 mm

So fractional error in radius is

Δrr=0.15=0.02\frac{\Delta r}{r} = \frac{0.1}{5} = 0.02rΔr​=50.1​=0.02

Thus,

Δvtvt=2(0.02)=0.04\frac{\Delta v_t}{v_t} = 2(0.02)=0.04vt​Δvt​​=2(0.02)=0.04

Therefore percentage error is

0.04×100=4%0.04 \times 100 = 4\%0.04×100=4%

Hence, Assertion A is true.

  1. Evaluate the options
  • A: A is false but R is true — incorrect
  • B: A is true but R is false — correct
  • C: Both true but R not explanation — incorrect
  • D: Both true and R correct explanation — incorrect
  1. Final conclusion

Assertion is true and Reason is false.

So the correct option is B.

PreviousNext

More from Properties of Matter

  • A wire of length ' L' and radius 'r' is clamped rigidly at one end. When the other end of the wire is pulled by a force f, its length increases by ' l'. Another wire of same material of length '2 L' and radius '2r'…2023 · MCQ
  • There is an air bubble of radius 1.0 mm in a liquid of surface tension 0.075 Nm−1 and density 1000 kg m−3 at a depth of 10 cm below the free surface. The amount by which the…2023 · Numerical
  • A 100 m long wire having cross-sectional area 6.25×10−4 m2 and Young's modulus is 1010 Nm−2 is subjected to a load of 250 N, then the elongation in the wire will be :2023 · MCQ
  • Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : Steel is used in the construction of buildings and bridges. Reason R : Steel is more elastic and its elastic limit is high.…2023 · MCQ
  • The frequency (u) of an oscillating liquid drop may depend upon radius (r) of the drop, density (ρ) of liquid and the surface tension (s) of the liquid as u=raρbsc. The values of a, b and c respectively are2023 · MCQ
  • A Spherical ball of radius 1mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. Viscous force on the ball when it attains constant velocity is 3696×10−x N. The value of x…2023 · Numerical
  • Match List I with List II Choose the correct answer from the options given below : Includes table2023 · MCQ
  • As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45 ∘ with the load axis. The length… Includes diagram2023 · Numerical