Question

A planet (having spherical shape) of uniform mass density is having double the mass of earth and radius same as that of earth. The acceleration due to gravity at the surface of this planet is [Acceleration due to gravity at the earth's surface is 10ms^-2]

• A. 10 ms^-2
• B. 5 ms^-2
• C. 20 ms^-2
• D. 40 ms^-2

Answer 1

The correct option is C

20 ms^-2

Assumptions and formulae:

Let M and R be the mass and radius of the earth

By definition, acceleration is due to gravity on earth's surface $g=\frac{GM}{R^2}$

Let $M_P$ and $R_P$ be the mass and radius of the planet

So, acceleration due to gravity on planet's surface $g_P=\frac{G{M}_P}{R_P}$

Given:

$M_P=2M$ and $R_P=R$

Hence, $g_P=\frac{G\left(2M\right)}{R}=2g$

Assume g=10 m/s ²

Therefore $g_P=20{\text{ms}}^{-2}$

Therefore right answer is option (C) 20 m/s^-2