Question

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 -

A
mg 2R
B
23mgR
C
3 mgR
D
13mgR

Solution

The correct option is B $$\displaystyle \frac{2}{3}mgR$$Mass = m, height = 2RAt height the acceleration due to gravity decreases , hence the value of acceleration due to gravity becomes g' = $$\dfrac{g}{1 + h/R}$$ = $$\dfrac{gR}{h + R}$$The value of potential energy  $$= mgh =\dfrac{mghR}{h + R}$$Now  $$h = 2R$$ (given)Henc change in potential energy = $$\dfrac{2}{3}$$mgRPhysics

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