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. $\left(\frac{1}{2}\right)mgR$ for $h=R$
• D. $(-\frac{1}{2})mgR$ for $h=R$

Answer 1

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

expression of potential energy on and above surface of earth is given by $-\frac{GMm}{r}$.

so when taken from surface to some height d then work required is $=-(-\frac{GMm}{R+d}+\frac{GMm}{R})$.

now if $d=R$ then expression reduces to $\frac{1}{2}mgR$.

expression is positive because work is to be done.