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 1 · 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 1 · Q48

Properties of Matter question

2023 · 13 Apr · Shift 1 · Q48

JEE MainPhysicsProperties of MatterMCQ+4 / −1
JEE Main 2023 (Online) 13th April Morning Shift Physics - Properties of Matter Question 93 English The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross - section. Cross sectional areas at A\mathrm{A}A is 1.5 cm21.5 \mathrm{~cm}^{2}1.5 cm2, and B\mathrm{B}B is 25 mm225 \mathrm{~mm}^{2}25 mm2, if the speed of liquid at B\mathrm{B}B is 60 cm/s60 \mathrm{~cm} / \mathrm{s}60 cm/s then (PA−PB)\left(\mathrm{P}_{\mathrm{A}}-\mathrm{P}_{\mathrm{B}}\right)(PA​−PB​) is : (Given PA\mathrm{P}_{\mathrm{A}}PA​ and PB\mathrm{P}_{\mathrm{B}}PB​ are liquid pressures at A\mathrm{A}A and B\mathrm{B}B% points. density ρ=1000 kg m−3A\rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}\mathrm{A}ρ=1000 kg m−3A and B\mathrm{B}B are on the axis of tube
  1. A
    27 Pa27 \mathrm{~Pa}27 Pa
  2. B
    175 Pa175 \mathrm{~Pa}175 Pa
  3. C
    135 Pa135 \mathrm{~Pa}135 Pa
  4. D
    36 Pa36 \mathrm{~Pa}36 Pa
View written solutionFree

Correct answer: B

  1. Use continuity equation

For steady flow in a horizontal tube, AAvA=ABvBA_A v_A = A_B v_BAA​vA​=AB​vB​

Given:

  • AA=1.5 cm2A_A = 1.5\,\text{cm}^2AA​=1.5cm2
  • AB=25 mm2=0.25 cm2A_B = 25\,\text{mm}^2 = 0.25\,\text{cm}^2AB​=25mm2=0.25cm2
  • vB=60 cm/sv_B = 60\,\text{cm/s}vB​=60cm/s

So, vA=ABAAvB=0.251.5×60=10 cm/sv_A = \frac{A_B}{A_A}v_B = \frac{0.25}{1.5}\times 60 = 10\,\text{cm/s}vA​=AA​AB​​vB​=1.50.25​×60=10cm/s

Convert to SI units: vA=0.1 m/s,vB=0.6 m/sv_A = 0.1\,\text{m/s}, \qquad v_B = 0.6\,\text{m/s}vA​=0.1m/s,vB​=0.6m/s

  1. Apply Bernoulli's equation

Since the tube is horizontal, gravitational terms cancel: PA+12ρvA2=PB+12ρvB2P_A + \frac{1}{2}\rho v_A^2 = P_B + \frac{1}{2}\rho v_B^2PA​+21​ρvA2​=PB​+21​ρvB2​

Therefore, PA−PB=12ρ(vB2−vA2)P_A - P_B = \frac{1}{2}\rho\left(v_B^2 - v_A^2\right)PA​−PB​=21​ρ(vB2​−vA2​)

Given ρ=1000 kg/m3\rho = 1000\,\text{kg/m}^3ρ=1000kg/m3, PA−PB=12(1000)[(0.6)2−(0.1)2]P_A - P_B = \frac{1}{2}(1000)\left[(0.6)^2 - (0.1)^2\right]PA​−PB​=21​(1000)[(0.6)2−(0.1)2] =500(0.36−0.01)= 500(0.36 - 0.01)=500(0.36−0.01) =500(0.35)= 500(0.35)=500(0.35) =175 Pa= 175\,\text{Pa}=175Pa

  1. Match with options

PA−PB=175 PaP_A - P_B = 175\,\text{Pa}PA​−PB​=175Pa

So the correct option is B.

PreviousNext

More from Properties of Matter

  • Under isothermal condition, the pressure of a gas is given by P=a V−3, where a is a constant and V is the volume of the gas. The bulk modulus at constant temperature is equal to2023 · MCQ
  • The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J. The cross sectional area of the wire is ​mm2. (…2023 · Numerical
  • Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : A spherical body of radius (5±0.1)mm having a particular density is falling through a…2023 · MCQ
  • 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