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. v_e
• B. 1.5v_e
• C. $\sqrt { 1.5 }$ v_e
• D. 2v_e

Answer 1

Answer: (C)

$\sqrt { 1.5 }$ v_e

Answer 2

Taking the potential at a large distance from the planet as zero, the potential at the centre of the planet = - $\frac { 3 \mathrm { GM } } { 2 \mathrm { R } }$ .

⇒ $\frac { 1 } { 2 } \mathrm { mv } ^ { 2 } = \mathrm { m } \left[ 0 - \left( - \frac { 3 \mathrm { GM } } { 2 \mathrm { R } } \right) \right]$ or v² = $\frac { 3 } { 2 }$v_e².

or v = $\sqrt { 1.5 }$v_e.