Question

A spherical planet far out in space has mass $M_0$ and diameter $D_0$. A particle of mass $m$ falling near the surface of this planet will experience acceleration due to gravity which is equal to

• A. $G{M}_0/D_0^2$
• B. $4Gm{M}_0/D_0^2$
• C. $4G{M}_0/D_0^2$
• D. $Gm{M}_0/D_0^2$

Answer 1

The correct option is C

$4G{M}_0/D_0^2$

Step 1: Given data

Mass of planet $=M_0$

Diameter $=D_0$

Mass of particle $=m$

Let Acceleration due to gravity $=g$

Let Gravitational constant $=G$

Let Radius of earth $=R$

Step 2: Find acceleration due to gravity

Acceleration due to gravity,

$g=G{M}_0/R^2$

Radius is

$R=D_0/2$

Thus, acceleration due to gravity become,

$g=4G{M}_0/D_0^2$

Hence, Option C is correct.