Question

A planet has a miss of eight times the mass of earth and density is also equal to eight times the average density of the earth. If g be the acceleration due to earth's gravity on its surface, then acceleration due to gravity on planet's surface will be :

• A. $2g$
• B. $4g$
• C. $8g$
• D. $16g$

Answer 1

The correct option is C $8g$

Let the density of the planet is $D_p$, the density of the earth is $D_e$, the mass of the planet is $M_p$ and the mass of the earth is $M_e$.

The density of the planet is given as,

$D_p=8D_e$

$\frac{M_p}{\frac{4}{3}\pi {R_p}^3}=8\times \frac{M_e}{\frac{4}{3}\pi {R_e}^3}$

$\frac{8M_e}{\frac{4}{3}\pi {R_p}^3}=8\times \frac{M_e}{\frac{4}{3}\pi {R_e}^3}$

$R_p=R_e$

The acceleration due to gravity is given as,

$\frac{g_p}{g_e}=\frac{\frac{G{M}_p}{{R_p}^2}}{\frac{G{M}_e}{{R_e}^2}}$

$\frac{g_p}{g}=\frac{\frac{8\times G{M}_e}{{R_p}^2}}{\frac{G{M}_e}{{R_e}^2}}$

$g_p=8g$

Thus, the acceleration due to gravity on the planet’s surface is $8g$.