Question

A planet has radius `1/4`th of the radius of earth and acceleration due to gravity double than that of the earth. Then the ratio of escape velocity on the surface of planet to that on the earth's surface will be ______.

Options

• `2sqrt2`

• `sqrt2`

• `1/sqrt2`

• 2

Answer 1

A planet has radius `1/4`th of the radius of earth and acceleration due to gravity double than that of the earth. Then the ratio of escape velocity on the surface of planet to that on the earth's surface will be `underline(1/sqrt2)`.

Explanation:

`"v"_e=sqrt(2gR)`

`"v"_e^'=sqrt(2xx2gxxR/4)=sqrt((2gR)/2)=V_e/sqrt2`

`becauseV_e^'/V_e=1/sqrt2`