Question

A body is projected vertically upwards from earth's surface with velocity 2v_e where v_e is escape velocity from earth's surface. The velocity when body escapes the gravitational pull is ______.

Options

• `sqrt5V_e`

• `sqrt7V_e`

• 2V_e

• `sqrt3V_e`

Answer 1

A body is projected vertically upwards from earth's surface with velocity 2v_e where v_e is escape velocity from earth's surface. The velocity when body escapes the gravitational pull is `underline(sqrt3V_e)`.

Explanation:

The kinetic energy given to the body = k `=1/2m(2V_e)^2`

`=1/2(4mV_e^2)`

The kinetic energy required to escape from the earth's gravitational field `=K^'=1/2mV_e^2`

If its velocity is V after escaping from the earth's gravitational field then its kinetic energy will be

`1/2mV^2=1/2(4mV_e^2)-1/2mV_e^2`

`=1/2(3mV_e^2)`

`thereforeV^2=3V_e^2`

`thereforeV=sqrt3V_e`