If the time period `(T)`of vibration of a liquid drop depends on surface tension `(S)` , radius`( r )` of the drop , and density `( rho )` of the liquid , then find the expression of `T`.

Options

A. `T = k sqrt(rho r^(3) //S)`
B. `T = k sqrt(rho^(1//2) rho^(3)//S)`
C. `T = k sqrt(rho r^(3) //S^(1//2))`
D. None of these

Answer

A

Explanation

(1) `T prop S^(a) rho^(b) rho^(c )`
`prop [MT^(-2)] [L]^(b) [ML^(-3)]^(c )`
`M^(0) L^(0) T^(1) prop M^(a + c) L^(b - 3c) T^(- 2a)`
`a+ c = 0, b - 3c = 0, -2a = 1`
`a = - (1)/(2), b = (3)/(2), c = (1)/(3)`
`T prop S^(-1//2) r^(3//2) rho^(1//2)`
`alpha sqrt((rho r^(3))/(S))`
`T = k sqrt((rho^(3))/(S))`
where `k` is a dimensionless constant.