Question

Density of a planet is two times the density of earth.Radius of this planet is half. (As compared to earth).

Column-I	Column-II
(a) Acceleration due to gravity on this planet surface	(p) Half
(b) gravitational potential on the surface	(q) Same
(c) Gravitational potential at centre	(r) Two time
(d) Gravitational field strength at centre	(s) Four time

• A. (a - p), (b - q), (c - r), (d - s)
• B. (a - q), (b - p), (c - p), (d - q)
• C. (a - s), (b - r), (c - q), (d - p)
• D. None of these

Answer 1

Answer: (B)

(a - q), (b - p), (c - p), (d - q)

$\text{Acceleration due to gravity on surface}=g=\frac{GM}{R^2}=\frac{G\rho \frac{4}{3}\pi R^3}{R^2}=\frac{4}{3}G\pi \rho R$

$\text{Density is doubled, radius is halved, so no change in acceleration due to gravity.}$

$\text{Gravitational potential at surface}=-\frac{GM}{R}=-\frac{4}{3}G\pi \rho R^2$

$\text{Therefore potential at surface is halved.}$

$\text{Gravitational potential at center}=-\frac{3GM}{2R}$

$\text{Therefore it is also halved.}$

$\text{Gravitational field strength at center=zero.}$

$\text{So it remains the same.}$