Two bodies of same masses are placed at
height h and 2 h. Compare their gravitational
potential energy
Answers
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.