Suppose the gravitational force varies inversely as the nth power of the distance. Then, the time period of a planet in circular orbit of radius fi around the sun will be proportional to
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a
Rn
b
R(n+1)/2
c
R(n−1)/2
d
R−n
answer is B.
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Detailed Solution
T=2πRV……………..(1)Further E=12mv2=GMmRn−1or V=2GMRn−11/2……..(2)From eqs. (1) and (2)T=2πR2GM/Rn−1=2π2GM×R(n+1)/2∝R(n+1)/2