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

Answer

A

Explanation

Let `T prop S^(0)t^(2) rho^(2)`
by substituting the demension of `[T]= [T]`
`[S] = [ML^(-2)], [r] = [L],= [ML^(-3)]`
and by comparing the power of both the sides
`x = -1//2, y = 3//2, z= 1//2`
so`T prop sqrt(rho r^(3)//S) rArr T = k sqrt((rho r^(3))/(S))`.