A planet whose mass and radius are both half of that of earth. Acceleration due to gravity(g) at its surface should be:

29.4 m / s e c^{2}

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19.6 m / s e c^{2}

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9.8 m / s e c^{2}

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4.9 m / s e c^{2}

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Solution

The correct option is B $19.6 m / s e c^{2}$
Acceleration due to gravity on earth, $g = \frac{G M}{R^{2}}$
Acceleration due to gravity on planet, $g^{'} = \frac{G (\frac{M}{2})}{(\frac{R}{2})^{2}} = 2 \frac{G M}{R^{2}} = 2 g = 19.6 m / s e c^{2}$

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A planet whose mass and radius are both half of that of earth. Acceleration due to gravity(g) at its surface should be:

The correct option is B 19.6m/sec2Acceleration due to gravity on earth,g=GMR2Acceleration due to gravity on planet,g′=G(M2)(R2)2=2GMR2=2g=19.6m/sec2

The correct option is B $19.6 m / s e c^{2}$
Acceleration due to gravity on earth, $g = \frac{G M}{R^{2}}$
Acceleration due to gravity on planet, $g^{'} = \frac{G (\frac{M}{2})}{(\frac{R}{2})^{2}} = 2 \frac{G M}{R^{2}} = 2 g = 19.6 m / s e c^{2}$