Question

The mass of a planet is double and its radius is half compared to that of earth. Assuming $g=10m/s^2$ on earth, the acceleration due to gravity at the planet will be :

• A. $10m/s^2$
• B. $20m/s^2$
• C. $40m/s^2$
• D. None of these

Answer 1

The correct option is D None of these

Using the relation, $g=\frac{GM}{R^2}$

Aceleration due to gravity at earth , $g_e=\frac{G{M}_e}{R_e^2}$...........(1)

Aceleration due to gravity at planet , $g_p=\frac{G{M}_p}{R_p^2}$ ............(2)

Given that $M_p=2M_e$, $R_p=\frac{1}{2}{R}_e$ , $g_e=10m/s^2$

Dividing (2) by (1) we get,
$\frac{g_p}{g_e}=\frac{M_p}{M_e}\times \frac{R_e^2}{R_p^2}=2\times (2{)}^2$

$g_p=8g_e$

$\therefore g_p=8\times 10=80m/s^2$.

Thus option D is correct.