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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`.

Text Solution

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Dimensions of time period = `[M^(0)L^(0)T^(1)]`
Dimensions of surface tension = `[M^(1)L^(0)T^(-2)]`
Dimensions of radius = `[M^(0)L^(1)T^(0)]`
Dimensions of density = `[M^(1)L^(-3)T^(0)]`
Now we have
`T=kS^(a)r^(b)rho^(c)`
`[M^(0)L^(0)T^(1)]=k[M^(1)L^(0)T^(-2)]^(a)[M^(0)L^(1)T^(0)]^(b)[M^(1)L^(-3)T^(0)]^(c)`
On comparing the coefficients, we get
`a=(-1)/(2),b=(3)/(2),c=(1)/(2)`
`T=ksqrt((rhor^(3))/(S))`
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