A planet has radius and mass, both half of that of the earth. The acceleration due to gravity on the planet will be

4.9 m / s^{2}

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9.8 m / s^{2}

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19.6 m / s^{2}

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13.8 m / s^{2}

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Solution

The correct option is C $19.6 m / s^{2}$
The acceleration due to gravity on the earth surface is given by
$g = \frac{G M}{R^{2}}$ . . . . . . . . . .(1)
Now, $M_{p} = \frac{M}{2}$ , $R_{p} = \frac{R}{2}$
The acceleration due to gravity on the planet is,
$g_{p} = \frac{G M_{p}}{R_{p}^{2}} = \frac{G M / 2}{R^{2} / 4} = 2 g$
$g_{p} = 2 \times 9.8 = 19.6 m / s^{2}$
The correct option is C.

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A planet has radius and mass, both half of that of the earth. The acceleration due to gravity on the planet will be

The correct option is C 19.6 m/s2The acceleration due to gravity on the earth surface is given byg=GMR2. . . . . . . . . .(1)Now, Mp=M2, Rp=R2The acceleration due to gravity on the planet is,gp=GMpR2p=GM/2R2/4=2g gp=2×9.8=19.6m/s2The correct option is C.