The mass of the moon is 1/144 times the mass of a planet and its diameter 1/16 times the diameter of a planet. If the escape velocity on the planet is v, the escape velocity on the moon will be:

Correct answer: (A) v/3. As we know, escape velocity is given by, v_escape=√2GMR Now, v_planet=√2GMR=v v_Moon=√(2GM×16144×R)=1/3√2GMR=v/3

Q68 / 90 · JEE Main 2024 (31 Jan Shift 2) · Physics

The mass of the moon is $\frac{1}{144}$ times the mass of a planet and its diameter $\frac{1}{16}$ times the diameter of a planet. If the escape velocity on the planet is v, the escape velocity on the moon will be:

As we know, escape velocity is given by, $v_{escape} = \sqrt{\frac{2 G M}{R}}$

Now, $v_{planet} = \sqrt{\frac{2 G M}{R}} = v$

$v_{Moon} = \sqrt{\frac{2 G M \times 16}{144 \times R}} = \frac{1}{3} \sqrt{\frac{2 G M}{R}} = \frac{v}{3}$

Hence, the correct answer is option: 'A'.