Question

A small mass 'm' is moved slowly from the surface of earth to a height 'h' from the surface. The work done (by external agent) in doing this is:

• A. mgh, for all values of h.
• B. mgh, for h << R
• C. $\frac{1}{2}$mgR for h = R
• D. $-\frac{1}{2}$mgR for h = R

Answer 1

The correct option is C $\frac{1}{2}$mgR for h = R

$P.E_1=\frac{-GMm}{R}=W_{1}P.E_2=\frac{-GMm}{(R+n)}=W_2\therefore △W=W_2-W_1=\frac{-GMm}{R}+\frac{-GMm}{(R+n)}=\frac{1}{2}\frac{GMm}{R}[ForR=h]=\frac{1}{2}mgR$