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If the time period (T)of vibration of a ...

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`.

A

`T = k sqrt((r^3 rho)/(S))`

B

`T = k sqrt((Srho)/(r^3))`

C

`T = k sqrt((r^3 )/(S rho))`

D

`T = k sqrt((r^3 S)/(rho))`

Text Solution

Verified by Experts

The correct Answer is:
A
We can say `T = k(S)^a (r)^b (rho)^c implies [T] = [MT^(-2)]^(a) [L]^(b)[ML^(-3)]^(c)`
We can say `a + c = 0`
`b - 3c = 0`
`- 2a = 1`
So, `a = 1/2 , c = + 1/2 & b = +3/2`
So `T = k (S)^(-1//2)(r)^(3//2)(rho)^(1//2) or T = k sqrt((r^3 rho)/(S))`
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