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A body A of mass m is moving in a circular orbit of radius R about a planet. Another body B of mass (m)/(2) collides with A with a velocity which is half ( v2 ) the instantaneous velocity v of A. The collision is completely inelastic. Then, the combined body:

continues to move in a circular orbit

Escapes from the Planet's Gravitational field

Falls vertically downwards towards the planet

Gravitation

JEE Main level, single correct, medium

189 of 223

Question 189 of 223

A body A of mass $m$ is moving in a circular orbit of radius $R$ about a planet. Another body B of mass $\dfrac{m}{2}$ collides with A with a velocity which is half $\left(\dfrac{\vec{v}}{2}\right)$ the instantaneous velocity $\vec{v}$ of A. The collision is completely inelastic. Then, the combined body:

Show answer and solution

Answer: (D) starts moving in an elliptical orbit around the planet

Conserving momentum

\dfrac{m}{2}\dfrac{v}{2}+mv=\left(m+\dfrac{m}{2}\right){v}_{f}

{v}_{f}=\dfrac{2mV}{4\times \dfrac{3m}{2}}=\dfrac{5V}{6}

{v}_{f}\lt {v}_{orb}\left(=v\right)

thus the combined mass will go on to an elliptical path

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JEE Main 2025 Apr 2 Shift 1 question paper

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