Solution :
$E= \large\frac{GM}{R^2}$
$\qquad= \large\frac{G\bigg(4/3 \pi R^3\rho\bigg)}{R^2}$
$\qquad=> E \alpha R$
$\large\frac{E_1}{E_2}= \frac{R_1}{R_2}= \frac{2R_2}{R_2}$$=2$
Hence a is not correct .
$\large\frac{E_1}{E_3}= \frac{3R_3}{R_3}$$=3$
So b is correct
Escape velocity $v= \sqrt { \large\frac{2GM}{R}}$
$\qquad= \sqrt {\large\frac{2G}{R} \normalsize \bigg( \frac{4}{3} \pi R^3 \rho)}$
$=> v \alpha R$
$ \large\frac{v_1}{v_3} =\frac{R_1}{R_2}$$=2$
$\therefore$ c is correct
$ \large\frac{v_1}{v_3} =\frac{R_1}{R_3}$$=3$
d is not correct .