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QNEET-2013-Ph-1495: NEET 2013 Physics - Class 11 NEET-2013-Ph-1495 Solution: A body of mass 'm' is taken from the earth's surface to the…
A body of mass 'm' is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be 3mgR mg2R
Multiple Choice Options
- A 3mgR
- B 3 1 _ mgR
- C mg2R
- D 3 2 _ mgR
Step-by-Step Verified Solution
Gravitational potential energy at any point at a distance r from the centre of the earth is
U = _ G M m r
where M and m be masses of the earth and the body respectively.
At the surface of the earth, r = R
U i = _ G M m R
At a height h from the surface,
r = R + h = R + 2R = 3R ( h = 2R (Given))
_ U f = _ G M m 3 R
Change in potential energy,
_ U = U f _ U i
= _ G M m 3 R _ ( _ G M m R ) = G M m R ( 1 _ 1 3 )
= 2 3 G M m R = 2 3 m g R ( _ g = G M R 2 )