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.
• C. $\frac { v _ { e } } { 2 }$
• D. Zero

Answer 1

Answer: (B)

Answer 2

Gravitational potential at the surface of the earth

$V _ { s } = - \frac { G M } { R }$

Gravitational potential at the centre of earth $V _ { c } = - \frac { 3 G M } { 2 R }$

By the conservation of energy $\frac { 1 } { 2 } m v ^ { 2 } = m \left( V _ { s } - V _ { c } \right)$

$= \frac { v _ { e } ^ { 2 } } { 2 }$ [As ]

$\therefore$ $v = \frac { v _ { e } } { \sqrt { 2 } }$