Suppose the gravitational force varies inversely as the nth power of distance. Then, the time period of a planet in circular orbit of radius r around the sun will be proportional to
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a
1r2(n+1)
b
1r2(n-1)
c
rn
d
1r2(n-2)
answer is A.
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Detailed Solution
As, gravitational force provides the necessary centripetal forcemv2r∝r-n⇒ v∝r(1-n)/2Also, T=2πrv or T∝rv-1or T∝r·r(n-1)/2or T∝r(n+1)/2
Suppose the gravitational force varies inversely as the nth power of distance. Then, the time period of a planet in circular orbit of radius r around the sun will be proportional to