The value of acceleration due to gravity on the earth is 10 m s − 2 . find the value of acceleration due to gravity

the value of acceleration due to gravity on the earth is 10 m s − 2 . find the value of acceleration due to gravity on the surface of a planet whose mass and radius both are four times that of earth.

Solution: 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 is given by

\LARGE g_e= \frac{G.M} {R^2}

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

\LARGE M_p= 4M

Radius of the planet is equal to 4 times the radius of earth.

\LARGE R_p= 4 R,

Let’s find the ratio of two planets to each other,

\LARGE \frac{g_p}{g_e}=\frac{\frac{4GM}{16R^2}}{\frac{GM}{R^2}}

result of the operation,

\LARGE g_p= \frac{4}{16}.g_e,

\LARGE g_e we know,

\LARGE g_e=10 m/s^2

\LARGE g_p= 10*\frac{4}{16} m/s^2=2.5m/s^2