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Gravitation Part 2

Section: Physics

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Question : 70 of 110

Marks: +1, -0

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:

[6-Apr-2023 shift 1]

$2^{\frac{1}{3}} W$
$2 W$
$W$
$2^{\frac{2}{3}} W$

Solution: 👈: Video Solution

Average Density of planet

=

average density of earth

\frac{M_e}{\frac{4}{3}\pi R_e^3} = \frac{M_p}{\frac{4}{3}\pi R_p^3}

\Rightarrow \frac{M_e}{R_e^3} = \frac{2M_e}{R_p^3}

\Rightarrow R_p = 2^{\frac{1}{3}} R_e\text{-------(i)}

\text{ Now, } g = \frac{GM}{R^2}

\frac{g_e}{g_p} = \frac{M_e}{R_e^2} \times \frac{R_p^2}{2M_e} = 2^{\frac{2}{3}-1} = 2^{-\frac{1}{3}}

\Rightarrow g_p = 2^{\frac{1}{3}} g_e

\Rightarrow W_p = 2^{\frac{1}{3}} W_e

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