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JEE Main 201912 JanuaryMorning Shift
Exam
JEE Main
Year
2019
Date
12 January
Shift
Morning Shift
Subject
Physics
Chapter
Gravitation

JEE Main 2019 · 12 January · Morning Shift · Physics · Gravitation

A satellite of mass M is in a circular orbit of radius R about the...

A satellite of mass MM is in a circular orbit of radius RR about the center of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastic. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be:A satellite of mass M is in a circular orbit of radius R about the center of the earth. A meteorite of the same mass,

Options

  1. AIn an elliptical orbit
  2. BSuch that it escapes to infinity
  3. CIn a circular orbit of a different radius
  4. DIn the same circular orbit of radius RR

Correct answer

A. In an elliptical orbit

Step-by-step solution

A satellite of mass M is in a circular orbit of radius R about the center of the earth. A meteorite of the same mass,

2mvx=mv2{mv}_{x} = mv

vx=v2{v}_{x} = \dfrac{v}{2}

Similarly vy=v2{v}_{y} = \dfrac{v}{2}

Vnet=(v2)2+(v2)2=v2{V}_{net} = \sqrt{{\left(\dfrac{v}{2}\right)}^{2} + {\left(\dfrac{v}{2}\right)}^{2}} = \dfrac{v}{\sqrt{2}}
As resultant velocity after collision is less than orbital velocity and it's direction is neither radial nor tangential , the combined mass will follow elliptical orbit

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