Question

The escape velocity for a planet is v_e. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be

(a) v_e

(b) v_e/√2

(c) v_e/2

(d) zero

Answer 1

Correct Answer is: (b) v_e/√2

v_e = √2Rg

At the surface of the planet, V_s = - GM/R

At the centre of the planet, V_c = - 3GM/2R

1/2mv² = m (V_s - V_c)

or v² = 2 GM/R (3/2 - 1) = GM/R =Rg = v_e²/2.