Question

If a planet consists of a satellite whose mass and radius were both half that of the earth, then the acceleration due to gravity at the surface of the planet would be

• A. $5.0m{s}^{-2}$
• B. $6.5m{s}^{-2}$
• C. $7.9m{s}^{-2}$
• D. $19.6m{s}^{-2}$

Answer 1

The correct option is D $19.6m{s}^{-2}$

Acceleration due to gravity, $g=\frac{GM}{R^2}$
$g\propto \frac{M}{R^2}$
For planet, $M_p=\frac{M_e}{2}$ and $R_p=\frac{R_e}{2}$
$\frac{g_p}{g_e}=\left(\frac{M_p}{M_e}\right){\left(\frac{R_e}{R_p}\right)}^2$
$=\left(\frac{1}{2}\right)\times (2{)}^2=2$
$g_p=2\times g_e=2\times 9.8=19.6m{s}^{-2}$.