Q142 / 180 · KCET 2010 · Physics
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?
- Correct answerABoth the mass and radius of the planet are half as that of earth
- BRadius of the planet is half as that of earth, but the mass is the same as that of earth
- CBoth the mass and radius of the planet are twice as that of earth
- DMass of the planet is half as that of earth, but radius is same as that of earth
Solution
Acceleration due to gravity on the surface of the planet is $g_{p}=\frac{G M_{p}^{2}}{R_{p}^{2}}$ Given, $\quad \mathrm{M}_{\mathrm{p}}=\frac{\mathrm{M}_{\mathrm{e}}}{2}$ and $\mathrm{R}_{\mathrm{p}}=\frac{\mathrm{R}_{\mathrm{e}}}{2}$
$$
\therefore \quad g_{p}=\frac{G(M e / 2)}{(\operatorname{Re} / 2)^{2}}=\frac{2 G M_{e}}{R_{e}}=2 g_{e}
$$
Hence, the correct answer is option: 'A'.