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Question
Two bodies of same masses are placed at heights h and 2h. Compare their gravitational potential energy.
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Solution 1
Gravitational pot. Energy of A: Gravitational pot.
energy of B = `(mgh)/(2mgh) = 1/2` = 1 : 2
Solution 2
The gravitational potential energy (GPE) of an object is given by the formula:
GPE = mgh
Where:
- m = mass of the object
- g = acceleration due to gravity
- h = height of the object
For the two bodies:
-
First body at height h:
GPE1 = mgh -
Second body at height 2h:
GPE2 = mg (2h) = 2mgh
Ratio of their GPEs:
`(GPE_1)/(GPE_2) = (mgh)/(2mgh) = 1/2`
The gravitational potential energy of the second body is twice that of the first body. Thus, GPE2 : GPE1 = 2 : 1.
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