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Q.

The period of revolution of a planet around the sun in circular orbit is same as that of period of similar planet revolving around a star of twice the radius of first orbit and ‘M’ is the mass of the sun and mass of star is

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a

2M

b

4M

c

8M

d

16M

answer is C.

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Detailed Solution

Gravitational force provide centripetal force, mrω2 =GMmr2 ⇒ω2=GMr3⇒ω=GMr3⇒2πT=GMr3⇒T=2πr3GMT∝r3M ⇒T2T1=r2r13M1M2⇒1=2r1r13M1M2⇒1=23M1M2⇒M2=8M1
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The period of revolution of a planet around the sun in circular orbit is same as that of period of similar planet revolving around a star of twice the radius of first orbit and ‘M’ is the mass of the sun and mass of star is