If a planet existed whose mass and radius wer | vedclass

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(D) The acceleration due to gravity $g$ on the surface of a planet is given by the formula $g = \frac{GM}{R^2}$,where $G$ is the gravitational constan

Vedclass · Accepted Answer

$19.6$

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(D) The acceleration due to gravity $g$ on the surface of a planet is given by the formula $g = \frac{GM}{R^2}$,where $G$ is the gravitational constant,$M$ is the mass of the planet,and $R$ is its radius.For Earth,$g_e = \frac{GM_e}{R_e^2} = 9.8 \, m s^{-2}$.For the new planet,the mass $M_p = \frac{M_e}{2}$ and the radius $R_p = \frac{R_e}{2}$.Substituting these values into the formula for the new planet's gravity $g_p$:$g_p = \frac{G(M_e/2)}{(R_e/2)^2} = \frac{G M_e / 2}{R_e^2 / 4} = 2 	imes \frac{GM_e}{R_e^2}$.Since $\frac{GM_e}{R_e^2} = g_e$,we have $g_p = 2 	imes g_e$.$g_p = 2 	imes 9.8 \, m s^{-2} = 19.6 \, m s^{-2}$.

If a planet existed whose mass and radius were both half that of the Earth,the acceleration due to gravity at its surface would be: (in $, m s^{-2}$)

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