The mass of a planet is 1 / 10^{th} that of the earth and its diameter is half that of the earth. The acceleration due to gravity

Question

The mass of a planet is \(\frac{1}{10}^{th}\) that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is: 

(1) \(19.6 \ m \ s^{–2} \)

(2) \(9.8 \ m \ s^{–2} \)

(3) \(4.9 \ m \ s^{–2} \)

(4) \(3.92\ m \ s^{–2}\)  

Answer 1

Correct option is : (4) \(3.92\ m\ s^{-2}\)

At Earth surface

\( g = \frac{GM}{R^2} = 9.8\ m/s^2\)

at given planet 

\( m' = \frac{m}{10}\) 

\(R' = \frac{R}{2}\)

\(g' = \frac{G\left(\frac{m}{10}\right)}{\left(\frac{R}{2}\right)^2} = 0.4g\)

\(g' = 3.92m/ s^2\)