Solved Example Problems for Fluids

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

Solved Example Problems for Pascal’s law

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