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

Answer

A

Explanation

`T prop S^(x) r^(y) rho^(z)`
`[T]=[MT^(-2)]^(x) [L]^(y) [ML^(-3)]^z`
`=[M^(x+z)L^(y-3z)T^(-2x)]`
`-2x =1 implies x =-1/2`
`y-3z =0implies y=3 xx1/2 =3/2`
`T prop S^(-1//2) r^(3//2) rho^(1//2)`
`T = ksqrt((rhor^(3)//S)`
Aliter :
Check Dimension in options.