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 $=9.8m/se{c}^2)$

• A. $4.9m/se{c}^2$
• B. $8.9m/se{c}^2$
• C. $19.6m/se{c}^2$
• D. $29.4m/se{c}^2$

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 $R_P=\frac{R_e}{2}$

$\therefore \frac{g_P}{g_e}=\left(\frac{M_P}{M_e}\right){\left(\frac{R_e}{R_p}\right)}^2=\left(\frac{1}{2}\right)\times {\left(2\right)}^2=2$

$\Rightarrow g_P=2g_e=2\times 9.8=19.6m{s}^2$