If a planet consists of a satellite whose mass and radius were both half that of the earth, the acceleration due to gravity at its surface would be ($g$ on earth $= 9.8\ m/s{ec}^{2}$)

Question

Dr. Abubacker · Accepted Answer

(c) $g = \frac{GM}{R^{2}}	herefore g \propto \frac{M}{R^{2}}$
According to problem $M_{p} = \frac{M_{e}}{2}$ and $R_{p} = \frac{R_{e}}{2}$
$	herefore\frac{g_{p}}{g_{e}} = \left( \frac{M_{p}}{M_{e}} ight)\left( \frac{R_{e}}{R_{p}} ight)^{2} = \left( \frac{1}{2} ight) 	imes (2)^{2} = 2$
$\Rightarrow g_{p} = 2g_{e} = 2 	imes 9.8 = 19.6\ m/s^{2}$

Q. If a planet consists of a satellite whose mass and radius were both half that of the earth, the acceleration due to gravity at its surface would be ($g$ on earth $= 9.8\ m/s{ec}^{2}$)

Explanation

Reviewed by Dr. Abubacker

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