Question

The escape velocity for a planet is $v_e$ A particle starts from rest at a large distance from the planet reaches the planet only under gravitational attraction and passes through a smooth tunnel through its centre Its speed at the centre of the planet will be

• A. $\sqrt{1.5}{v}_e$
• B. $\frac{v_e}{\sqrt{2}}$
• C. $v_e$
• D. zero

Answer 1

Answer: (A)

$\sqrt{1.5}{v}_e$

From mechanical energy conservation 0 + 0 = $\frac{1}{2}m{v}^2-\frac{3GMm}{2R}\Rightarrow v=\sqrt{\frac{3GM}{R}}=\sqrt{1.5}{v}_e$