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Mass density of sphere of radius R is (K...

Mass density of sphere of radius `R` is `(K)/(r^(2))`. Where `K` is constant and `r` is distance from centre. A particle is moving near surface of sphere along circular path of radius R with time period T. Then

A

T/R is constant

B

TR is constant

C

`T^(2)//R^(3)` is a constant

D

`T//R^(2)` is a constant

Text Solution

Verified by Experts

The correct Answer is:
A
`rho (r ) = (K)/(r^(2)) (Mv^(2))/(R ) = (GM)/(R )`
`(Mv^(2))/(R ) = (G int_(0)^(R ) rho (r ) 4 pi r^(2) dn)/(R^(2)), m ((2 pi)/(T))^(2) R = (GK 4 pi R)/(R^(2))`
`(T)/(R )` = constant
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