1.

Imagine a light planet 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 planet and the star is proportional to R^(-5//2), then T^2 is proportional to

Answer»

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

Solution :For motion of PLANET in a circular orbit,
CENTRIPETAL force = GRAVITATIONAL force
or `mRomega^2 = (GmM)/R^(5//2)` or `R^(7//2)omega^2=GM`
`R^(7//2)=(GM)/omega^2 =(GM)/(2pi//T)^2 =(T^2xxGM)/(4pi^2)` or `T^2 PROP R^(7//2)`


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