The escape velocity for a planet is ve. A particle starts from rest at

1.	The escape velocity for a planet is ve. 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) ve (b) 1.5ve(c) √1.5 ve(d) 2ve
Answer» Correct Answer is: (c) √1.5 v Taking the potential at a large distance from the planet as zero, the potential at the centre of the planet = - 3GM/2R ∴ 1/2 mv² = m [ 0 - (- 3GM/2R)] or v² = 3GM/2R = 3Rg = 3/2 (2RG) = 3/2 v_e² or v = √1.5 v_e .

The escape velocity for a planet is ve. 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) ve (b) 1.5ve(c) √1.5 ve(d) 2ve

Answer»

Correct Answer is: (c) √1.5 v

Taking the potential at a large distance from the planet as zero, the potential at the centre of the planet = - 3GM/2R

∴ 1/2 mv² = m [ 0 - (- 3GM/2R)]

or v² = 3GM/2R = 3Rg = 3/2 (2RG) = 3/2 v_e²

or v = √1.5 v_e .