Answer :

• Ratio of the gravitational potential energy of the two bodies = 1 : 2

Explanation :

GIVEN :

• Mass of the both the bodies, m₁ = m₂ = m
• Height of the first body, h₁ = h
• Height of the SECOND body, h₂ = 2h
• Acceleration due to gravity, g = 10 m/s².

To FIND :

• Ratio of the gravitational potential energy of the two bodies.

Knowledge required :

Formula for Potential energy of a body :

⠀⠀⠀⠀⠀⠀⠀⠀⠀P.E. = mgh

Where,

• P.E. = Potential energy of the body.
• m = Mass of the body.
• g = Acceleration due to gravity acting on the body.
• h = Height at which the body is kept.

Solution :

First LET us find the Potential energy of the body at height of h.

By using the formula for potential energy possessed by a body and substituting the values in it, we get :

⠀⠀=> P.E. = mgh₁

⠀⠀=> P.E. = m × 10 × h

⠀⠀=> P.E. = 10mh

⠀⠀⠀⠀⠀⠀∴ P.E. = 10mh

Hence the potential energy possessed by the body at HIEGHT = h, is 10mh

Now let's find out the potential energy possessed by the body at height of 2h.

By using the formula for potential energy possessed by a body and substituting the values in it, we get :

⠀⠀=> P.E. = mgh₁

⠀⠀=> P.E. = m × 10 × 2h

⠀⠀=> P.E. = 20mh

⠀⠀⠀⠀⠀⠀∴ P.E. = 20mh

By comparing them, we get :

⠀⠀=> P.E.₁/P.E.₂

By substituting the values in it, we get :

⠀⠀=> P.E.₁/P.E.₂ = 10mh/20mh

⠀⠀=> P.E.₁/P.E.₂ = 1/2

⠀⠀=> P.E.₁ : P.E.₂ = 1 : 2

⠀⠀⠀⠀⠀⠀⠀∴ P.E.₁ : P.E.₂ = 1 : 2

Hence the ratio of the potential energy possessed by the body at height , h and 2h is 1 : 2.