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JEE Main202523 Jan 2025Evening ShiftPhysicsGravitationActual

A satellite of mass M 2 is revolving around earth in a circular orbit at a height of R 3 from earth surface. The angular momentum of the satellite is M G M R x . The value of x is ______ , where M and R are the mass and radius of earth, respectively. ( G is the gravitational constant)

Correct answer

0

Step-by-step solution

aligned & orbital velocity v₀= GM 4 R / 3 = 3 GM 4 R & Angular momentum of satellite = M 2 v ₀ 4 R 3 & = M 2 3 GM 4 R 4 R 3 & =M GMR 3 & x=3 aligned (ii) Since mass of satellite is comparable to the mass of earth. aligned & G.M. M 2 ( 4 R 3 )^2 = M 2 ^2 8 R 9 & = 81 GM 128 R ^3 aligned Angular momentum of satellite about common centre of mass, aligned & L= M 2 ( 8 R 9 )^2 & L=M GMR ( 8 81 ) & x= 81 8 10 aligned

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