Question

A body of mass is taken from earth surface to the height $h$ equal to twice the radius of earth $\left(R_e\right)$. the inerease in potential energy will be: ( $g$ = acceleration due to gravity on the surface of Earth)

• A. $\frac{1}{2} m g R_e$
• B. $3 m g R_e$
• C. $\frac{2}{3} m g R_e$
• D. $\frac{1}{3} m g R_e$

Answer 1

Answer: (C)

$ U =\frac{- GM _{ e } m }{ r } $
$ U _{ i }=\frac{- GM _{ e } m }{ R _{ e }} $
$ U _{ f }=\frac{- GM _{ e } m }{\left( R _{ e }+ h \right)}=\frac{- GM _{ e } m }{ R _{ e }+2 R _{ e }}$
$\frac{- GM _{ e } m }{3 R _{ e }}$
Increase in internal energy $\Delta U = U _{ f }- U _{ i }$
$ =\frac{2}{3} \frac{ GM _{ e } m }{ R _{ e }} $
$\frac{2}{3} \frac{ GM _{ e }}{ R _{ e }^2} mR _{ e } $
$=\frac{2}{3} mgR _{ e }$