Question

A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is $V$. Due to the rotation of a planet about its axis the acceleration due to gravity $g$ at equator is $\frac{1}{2}$ of $g$ at poles. The escape velocity of a particle on the pole of a planet in terms of $V$ is

• A. $V_e=2V$
• B. $V_e=V$
• C. $V_e=\frac{V}{2}$
• D. $V_e=\sqrt{3}V$

Answer 1

The correct option is A $V_e=2V$

$V=\omega R$
$g=g_0-{\omega }^{2}R(g=atequator,g_0=atpoles)$
$\frac{g_0}{2}=g_0-{\omega }^{2}R;{\omega }^{2}R=\frac{g_0}{2};V^2=\frac{g_{0}R}{2}$
$v_e=\sqrt{2g_{0}R}=\sqrt{4V^2}=2V$