Q. The escape velocity of a body on the earth’s surface is $v_{e}$. A body is thrown up with a speed $\sqrt{5}\ v_{e}$. Assuming that the sun and planets do not influence the motion of the body, velocity of the body at infinite distance is
A) Zero
B) $v_{e}$
C) $\sqrt{2}v_{e}$
D) ${2v}_{e}$
Explanation
(d) Since, velocity of projection $(v)$is greater than the escape velocity $\left( v_{e} \right),$therefore at infinite distance the body moves with a velocity
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v^{'} = \sqrt{v^{2} - v_{e}^{2}}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ v^{'} = \sqrt{(\sqrt{5}v_{e})^{2} - v_{e}^{2}} = 2v_{e}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.