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Suppose the gravitational force varies i...

Suppose the gravitational force varies inversely as the `n^(th)` power of distance. Then the time period of a planet in circular orbit of radius `r` around the sun will be proportional to

Text Solution

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`(GMm)/(R^(n))=mR(pi/R_(2))^(2)`
or `T^(2)=(Rxx4pi^(2)xxR^(n))/(GM)=(4pi^(2)R^(n+1))/(GM)`
or `T=(2pi)/sqrt((GM))r^((n+1)/2)`
or `TpropR^((n+1)/2)`
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