Question

The acceleration due to gravity on the surface of a planet, whose mass and diameter are double that of the earth, is _____ times the acceleration due to gravity on the surface of the earth.

• A. $1$
• B. $0.5$
• C. $2$
• D. $0.25$

Answer 1

The correct option is B $0.5$

Acceleration due to the gravity at the surface of the earth $=g_e=\frac{G{M}_e}{R_e^2}$

It is given that $M_p=2M_e,R_p=2R_e$

Acceleration due to the gravity at the surface of the planet $g_p=\frac{G{M}_p}{R_p^2}=\frac{G\left(2M_e\right)}{(2R_e{)}^2}=\frac{G{M}_e}{2R_e^2}=\frac{g_e}{2}$

Hence correct answer is option $B$