Question

Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g', then:

• A. $g^{\prime }=3g$
• B. $g^{\prime }=\frac{g}{3}$
• C. $g^{\prime }=9g$
• D. $g^{\prime }=27g$

Answer 1

The correct option is A $g^{\prime }=3g$

Acceleration due to gravity at the surface, $g=\frac{GM}{R^2}$

Mass of planet, $M=\rho \times \frac{4\pi }{3}{R}^3$ where R is the radius of planet.

$⟹g=\frac{4\pi }{3}G\rho R$

As radius of new planet, $R^{\prime }=3R$

$⟹g^{\prime }=3g$