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Q.

$g_{e} {and g}_{p}$ denote the acceleration due to gravity on the surface of earth and another planet whose mass and radius are twice that of the earth, then

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a

g_{p} = 2 g_{e}

b

g_{p} = g_{e}

c

g_{p} = g_{e} /2

answer is B.

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Detailed Solution

g = \frac{GM}{R^{2}} [\begin{matrix} m_{p} = 2 m_{e} \\ R_{e} = 2 R_{e} \end{matrix}]

$\frac{g_{e}}{g_{p}} = \frac{m_{e}}{m_{p}} \times \frac{R_{p}^{2}}{R_{e}^{2}}$

$\frac{g_{e}}{g_{p}} = \frac{m_{e}}{2 m_{e}} \times \frac{4 R_{e}^{2}}{R_{e}^{2}}$

$g_{e} = 2 g_{p}$

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