Question

Match the following list 1 to list 2

Answer 1

(a) $W=\Delta U=\frac{mgh}{1+\frac{h}{R}}$

Put $h=R$, $W=\frac{1}{2}mgR$

(b) $K.E.=\frac{GMm}{2r}=\frac{GMm}{4R}=\frac{1}{4}mgR$ (as $GM=g{R}^2$)

(c) $E=-\frac{GMm}{2r}$

$E_1=-\frac{GMm}{2\left(2R\right)}$

$=-\frac{GMm}{4R}=-\frac{1}{4}mgR$

$E_2=-\frac{GMm}{2\left(3R\right)}=-\frac{1}{6}mgR$

$E_1-E=\frac{1}{12}mgR$

(d) $K.E.=\Delta U=\frac{mgh}{1+\frac{h}{R}}$

Putting h=R, $K.E.=\frac{1}{2}mgR$