Question

A block of volume V and of density σ_b is placed in liquid of density σ₁(σ₁>σ_b), then block is moved upward up to a height h and it is still in liquid . The increase in gravitational potential energy of the block is

Answer 1

Gravitational potential energy is defined as the energy possessed by a body by virtue of its motion under the gravitational field. As the acceleration due to gravity is constant near the surface so the gravitational potential energy of an object at a height h is given by

U = m x g x h

Where m = mass of the block, h = change in height of block, g = acceleration due to gravity.

The zero point of gravitational potential energy can be chosen as any point like that of a coordinate system.

As the gravitational potential energy of an object of mass m only depends upon the position and acceleration due to gravity and independent upon the medium it is placed so the change in gravitational potential energy will be equal in a liquid medium and air medium.

Let the block has mass m, is initially at height h₁ from the ground and its height changes to h₂, where (h₂ − h₁ = h)

Change in potential energy of the block when height changes from h₁ to h₂

ΔU = final potential energy − initial potential energy

= mgh₂ − mgh₁

= mg(h₂−h₁)

= mgh

Because (h₂ − h₁ = h)

Mass of the block

= density of block × volume of block

= σ_b×V

Now Change in potential energy is given by

ΔU = mgh = σ_bV × gh = σ_bVgh