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

Let `TpropS^xr^yrho^z`
by subsituting the dimension of `[T]=[T]`
`[S]=[MT^-2]`,`[r]=[L]`,`[rho]=[ML^-3]`
and by comparing the power of both sides
`x=(-1)/(2)`,`y=(3)/(2)`,`z=(1)/(2)`
So `Tpropsqrt((rhor^3)/(S))impliesT=ksqrt((rho^3)/(S))`