1.

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`.

Answer» Let `T prop S^(x) r^(y) rho ^(z) or T = K S^(x) r^(y) rho^(z)`
By substituting the dimension of each quantity in both sides, `[M^(0) L^(0) T^(1)] = K [MT^(-2)]^(x) [L]^(y) [ML^(-3)]^(z) = [M^(x+ z) L^( y - 3z) T^(-2x)]` By equating the power of M, L , and T in both sides,
By solving above three equations , we get
`x = -1//2 , y = 3//2 , z = 1//2`
So the time period can be given as
`T = KS^(-1//2) r^(3//2) rho^(1//2) = K sqrt( rho r^(3)/( S))`


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