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# Solved Example Problems for Fluids

Physics : Properties of Matter - Solved Example Problems for Pascal’s law, Buoyancy

### EXAMPLE 7.6

A solid sphere has a radius of 1.5 cm and a mass of 0.038 kg. Calculate the specific gravity or relative density of the sphere.

### Solution

Radius of the sphere R = 1.5 cm

mass m = 0.038 kg ### EXAMPLE 7.7

Two pistons of a hydraulic lift have diameters of 60 cm and 5 cm. What is the force exerted by the larger piston when 50 N is placed on the smaller piston?

### Solution

Since, the diameter of the pistons are given, we can calculate the radius of the piston This means, with the force of 50 N, the force of 7200 N can be lifted.

Solved Example Problems for Buoyancy

### EXAMPLE 7.8

A cube of wood floating in water supports a 300 g mass at the centre of its top face. When the mass is removed, the cube rises by 3 cm. Determine the volume of the cube.

### Solution

Let each side of the cube be l. The volume occupied by 3 cm depth of cube,

V=(3cm) × l2 = 3l2cm

According to the principle of floatation, we have

Vρg = mg  Vρ = m

ρ is density of water = 1000 kg m-3

(3l2 × 10-2m) × (1000 kgm-3)=300 × 10-3 kg l = 10 × 10-2m = 10 cm

Therefore, volume of cube V = l3 = 1000 cm3

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