Question

If a planet consists of a satellite whose mass and radius were both half that of the earth, the acceleration due to gravity at its surface would be ($g$ on earth $= 9.8 \,m/sec^2)$

• A. $4.9 \,m/sec^2$
• B. $8.9 \,m/sec^2$
• C. $19.6 \,m/sec^2$
• D. $29.4 \,m/sec^2$

Answer 1

Answer: (C)

$g = \frac{GM}{R^2} $
$\therefore g \propto \frac{M}{R^2}$
According to problem $M_P = \frac{M_e}{2}$
and $R_P = \frac{R_e}{2}$
$\therefore \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\left(2\right)^{2} = 2 $
$\Rightarrow g_{P} = 2g_{e} = 2\times9.8 = 19.6 \,ms^{2}$