KCET · Physics · Gravitation
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 half as that of earth
- B Radius of the planet is half as that of earth, but the mass is the same as that of earth
- C Both the mass and radius of the planet are twice as that of earth
- D Mass of the planet is half as that of earth, but radius is same as that of earth
Answer & Solution
Correct Answer
(A) Both the mass and radius of the planet are half as that of earth
Step-by-step Solution
Detailed explanation
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 \(\mathrm{R}_{\mathrm{p}}=\frac{\mathrm{R}_{\mathrm{e}}}{2}\)
\(\therefore g_{p}=\frac{G(M e / 2)}{(\operatorname{Re} / 2)^{2}}=\frac{2 G M_{e}}{R_{e}}=2 g_{e}\)
\(\therefore g_{p}=\frac{G(M e / 2)}{(\operatorname{Re} / 2)^{2}}=\frac{2 G M_{e}}{R_{e}}=2 g_{e}\)
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