The escape velocity for a planet is ve. A tunnel is dug along a diamet

1.	The escape velocity for a planet is ve. 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) ve(b) ve/√2(c) ve/2(d) zero
Answer» 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.

The escape velocity for a planet is ve. 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) ve(b) ve/√2(c) ve/2(d) zero

Answer»

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.