Q.

Assume the planetary orbits to be circular and T be the time period of revolution of the earth around the sun of mass M. If the Jupiter’s period of revolution around the sun is K times that of the earth, the velocity of Jupiter in heliocentric reference frame is 2πGMTK1/y1/x.The product of x and y is

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answer is 3.

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Detailed Solution

TJT2=RJR3=K2

RJ=K2/3R..(1)

For earth:

 GMmeR2=meR4π2T2
T2=4π2R3GM

R=T2GM4π21/3............(2)

For Jupiter:
GMmJRJ2=mJV2RJ

V=GMRJ=GMK2/3R

V=2πGMTK1/3

xy=3

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Assume the planetary orbits to be circular and T be the time period of revolution of the earth around the sun of mass M. If the Jupiter’s period of revolution around the sun is K times that of the earth, the velocity of Jupiter in heliocentric reference frame is 2πGMTK1/y1/x.The product of x and y is