Question

Two stones, one with twice the mass of the other, are thrown straight up and rise to the same height h. Compare their changes in gravitational potential energy.

Answer 1

The gravitational potential energy is double for stone with twice the mass of other stone.

Explanation:

Let mass of stone 1 be m.

Mass of stone 2 is twice the mass of stone 1.

Mass of stone 2 = 2m

We know that

  Gravitational potential energy = Mass x acceleration due to gravity x Height

  PE = mgh

For stone 1 ,

                PE₁ = mgh

For stone 2 ,

                PE₂ = 2mgh = 2 PE₁

So the gravitational potential energy is double for stone with twice the mass of other stone.

               

Answer 2

Answer:

 P.E₂ =  2 P.E₁

Explanation:

mass of stone 1 , m₁= m

mass of stone 2, m₂ = 2 m

rise of stone 1,  h₁ = h

rise of stone 2,  h₂ = h

Potential energy of the stone 1

P.E₁ = m₁ g h₁

P.E₁ = m g h

Potential energy of stone 2

 P.E₂ = m₂ g h₂

 P.E₂ =  2 m g h

now,

 P.E₂ =  2 P.E₁

Potential energy of the stone 2 is twice potential energy of the stone 1.