Question

An astronaut on a strange planet finds that acceleration due to gravity is twice as that on the surface of Earth. Which of the following could explain this?

• A. Both the mass and radius of the planet are twice as that of Earth.
• B. Mass of the planet is half as that of Earth, but radius is same as that of Earth.
• C. Both the mass and radius of the planet are half as that of Earth.
• D. Radius of the planet is half as that of Earth, but the mass is the same as that of Earth

Answer 1

Answer: (C)

Acceleration due to gravity on the surface of the planet is $g_{p}=\frac{G M_{p}^{2}}{R_{p}^{2}}$
Given, $\quad M_{p}=\frac{M_{e}}{2}$
and $R_{p}=\frac{R_{e}}{2}$
$\therefore g_{p}=\frac{G(M e / 2)}{(R e / 2)^{2}}=\frac{2 G M_{e}}{R_{e}}=2 g_{e}$