Question

A cylinder of area 300 cm² and length 10 cm made of material of specific gravity 0.8 is floated in water with its axis vertical. It is then pushed downward, so as to be just immersed. The work done by the agent who pushes the cylinder into the water is ______ J.

Options

• 0.01

• 0.02

• 0.05

• 0.06

Answer 1

A cylinder of area 300 cm² and length 10 cm made of material of specific gravity 0.8 is floated in water with its axis vertical. It is then pushed downward, so as to be just immersed. The work done by the agent who pushes the cylinder into the water is 0.06 J.

Explanation:

Weight of cylinder

= 300 × 10^–4 × 10 × 10^–2 × 800 g

= 2.4 g

Let x is the length of cylinder inside water.

Then

2.4 g = 300 × 10^–4 × x × 1000 g

x = 0.08 m

When completely immersed buoyant force

F_b = 300 × 10^–4 × 0.1 × 1000 g

F_b = 3 gN

Hence in order to immerse the cylinder in water, an external agent must push it 0.02 m against the average upward thrust.

Increase in upward thrust

= 3 g – 2.4 g = 0.6 g N.

Because this increase occurs gradually, we take the average upward thrust against which work is done.

∴ Work done = 0.3 g × 0.02

= 0.3 × 10 × 0.02

= 0.06 J