A body of mass 2 m is placed on earth's surface. Calculate the change in gravitational potential energy, if this body is taken from earth's surface to a height of h , where h=4 R .

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Correct answer: C. (8)/(5) m g R

Potential energy, U=-(G M m)/(r)=(-2 G M m)/(r) [ m=2 m] At earth's surface, r=R U_e=-(2 G M m)/(R) Now, if a body is taken to height, h=4 R , then the potential energy is given by aligned U_h & =-(2 G M m)/(R+h) [ r=h+R] & =(-2 G M m)/(5 R) aligned Thus, change in gravitational potential energy, aligned Δ U & =U_h-U_e & =-(2 G M m)/(5 R)+(2 G M m)/(R)=(8)/(5) (G M m)/(R) aligned aligned Δ U & =(8)/(5) (g R^2 m)/(R) [ G M=g R^2] & =(8)/(5) m g R aligned

A body of mass 2 m is placed on earth's surface. Calculate the...

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