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Mechanical Properties of Fluids · Question 27

JEE Main 2025 (Online) 2nd April Morning ShiftNumericalMedium📈 Topic in 6% papers+4
1

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of 100 cm2 with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density 1.5 103 kg/m3. What force one needs to apply on the hinged door so that it does not get opened? (Acceleration due to gravity = 10 m/s2)

Answer

150

Solution

Small window use the pressure at depth h = 3 m (atmospheric pressure cancels).

Water side: P1 = 1 gh = 103 10 3 = 3 104 Pa

Liquid side: P2 = 2 gh = 1.5 103 10 3 = 4.5 104 Pa

Net force: F = (P2 - P1)A = 1.5 104 100 10-4

F = 150 N (applied from the water side)

Answer: 150

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2

Two water drops each of radius 'r' coalesce to form a bigger drop. If 'T' is the surface tension, the surface energy released in this process is :

  1. 4 r2 T [2 - 21/3 ]
  2. 4 r2 T[1 + 2]
  3. 4 r2 T [2 - 22/3 ]
  4. 4 r2 T[ 2 - 1]
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3

In a hydraulic lift, the surface area of the input piston is 6 cm2 and that of the output piston is 1500 cm2. If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is kJ.

JEE Main 2025 (Online) 29th January Morning Shift
4

Consider following statements: Choose the correct answer from the options given below:

  1. B, C, D Only
  2. C, D, E Only
  3. A, D, E Only
  4. A, B, C Only
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5

A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water? (Given: density of water = 1000 kg m-3)

  1. 400 cm3
  2. 600 cm3
  3. 1400 cm3
  4. 4000 cm3
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