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
Correct Answer: A
Solution :
Acceleration due to gravity on the surface of the planet is \[{{g}_{p}}=\frac{G{{M}_{p}}}{R_{p}^{2}}\] Given, \[{{M}_{p}}=\frac{{{M}_{e}}}{2}\] and \[{{R}_{p}}=\frac{{{R}_{e}}}{2}\] \[\therefore \] \[{{g}_{p}}=\frac{G(Me/2)}{{{(\operatorname{Re}/2)}^{2}}}=\frac{2G{{M}_{e}}}{{{R}_{e}}}=2{{g}_{e}}\]
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