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JEE Main 2023 (6 Apr, Shift 1) · Acceleration Due to Gravity

Acceleration Due to Gravity question from JEE Main 2023 (6 Apr, Shift 1)

Q65JEE Main 2023 · 6 APR · SHIFT 1Medium

Acceleration Due to Gravity

A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing $W$ on earth will weigh on that planet:

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Answer: (d)

$M = \frac{4}{3}\pi R^3\rho$ ; same $\rho$ and $M_p = 2M \Rightarrow R_p = 2^{1/3}R$ .
$g = \frac{GM}{R^2} = \frac{4}{3}\pi G\rho R \Rightarrow g \propto R$
$g_p = 2^{1/3}g$ , so weight $= 2^{1/3}W$ .
So the answer is (d) $2^{1/3}\text{ W}$ .

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