1.

A light planet is revolving around a very massive star in a circular orbit of radius R with a period of revolution T, if the gravitational force of attraction between the two varies as R^(-5//2), then T^(2) is proportional to :

Answer»

`R^(3)`
`R^((7)/(2))`
`R^((3)/(2))`
`R^((5)/(2))`

Solution :Here `(MV^(2))/(R )=(GMm)/(R^(5//2)) rArr v^(2)=(GM)/(R^(3//2))`
Now `T=(2PI R)/(v) therefore T^(2)=(4pi^(2)R^(2))/(v^(2))`
`T^(2)=(4pi^(2)R^(2)xxR^(3//2))/(GM) rArr T^(2)prop R^(7//2)`
Thus correct choice is (b).


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