If a planet has a mass and radius both half t | vedclass

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(C) The acceleration due to gravity on the surface of a planet is given by the formula $g = \frac{GM}{R^2}$.This implies that $g \propto \frac{M}{R^2}

Vedclass · Accepted Answer

$19.6$

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(C) The acceleration due to gravity on the surface of a planet is given by the formula $g = \frac{GM}{R^2}$.This implies that $g \propto \frac{M}{R^2}$.According to the problem,the mass of the planet is $M_p = \frac{M_e}{2}$ and its radius is $R_p = \frac{R_e}{2}$,where $M_e$ and $R_e$ are the mass and radius of the Earth respectively.Taking the ratio of the acceleration due to gravity on the planet $(g_p)$ to that on Earth $(g_e)$:$\frac{g_p}{g_e} = \left( \frac{M_p}{M_e} ight) 	imes \left( \frac{R_e}{R_p} ight)^2 = \left( \frac{1}{2} ight) 	imes (2)^2 = \frac{1}{2} 	imes 4 = 2$.Therefore,$g_p = 2 	imes g_e = 2 	imes 9.8\, m/s^2 = 19.6\, m/s^2$.

If a planet has a mass and radius both half that of the Earth,the acceleration due to gravity at its surface would be ......... $m/s^2$ ($g$ on Earth $= 9.8\, m/s^2$)

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