Question

Acceleration due to gravity at earth's surface is $10 \, m \, s^{- 2}$ . The value of acceleration due to gravity at the surface of a planet of mass $\frac{1}{5}$ th and radius $\frac{1}{2}$ of the earth is -

• A. $4 \, m \, s^{- 2}$
• B. $6 \, m \, s^{- 2}$
• C. $8 \, m \, s^{- 2}$
• D. $12 \, m \, s^{- 2}$

Answer 1

Answer: (C)

$g_{p}=\frac{G M_{p}}{R_{P}^{2}}$
$M_{p}=\text{mass of planet}$
$R_{p}=\text{radius of planet }$
$g_{p}=\text{Acceleration due to gravity on planet}$
$g_{p}=\frac{G \left(\frac{M_{e}}{5}\right)}{\left(\frac{R_{e}}{2}\right)^{2}}$
$=G\times \frac{1}{5}\times M_{e}\times \frac{4}{R_{e}^{2}}$
$=\frac{4}{5}g=8 \, m s^{- 2}$