Question

Calculate the value of acceleration due to gravity on a planet whose mass is 4 times as that of the earth and radius is 3 times as that of the earth.

Answer 1

If M is the mass of the earth and R is the radius of earth, the value of acceleration due to gravity on the earth ($g_e$) is given by

$g_e$ = $\frac{GM}{R^2}$ ......(1)

Let us consider a planet such that mass of the planet is equal to 4 times the mass of the earth.

$M_p$ = 4M

Radius of the planet is equal to 3 times the radius of earth.

$R_e$ = 3 R

Then, acceleration due to gravity on this planet ($g_p$) is

$g_p$ = $\frac{G\ast \left(4M\right)}{{3R}^2}$ = $\frac{4}{9}$ $\frac{GM}{R^2}$ .......(2)

Dividing equation (2) by equation (1), we get

$\frac{g_p}{g_e}$ = $\frac{\frac{4}{9}\frac{GM}{R^2}}{\frac{GM}{R^2}}$ or $\frac{g_p}{g_e}$ = $\frac{4}{9}$

or $g_p$ = $\frac{4}{9}$ ($g_e$)

Since $g_e$ = 9.8 $\frac{m}{{sec}^2}$

$g_p$ = $\frac{4}{9}$ * 9.8 = 4.35 $\frac{m}{{sec}^2}$

Thus, acceleration due to gravity on the given planet is 4.35 $\frac{m}{sec}$ .