A sphere of incompressible liquid is distorted from the sphericial form and released. Deduce by the method of dimensions an expression for the period of its subsequent oscillantions assuming that the only forces which need to be considered arise from its own surface tension.

Answer

`T=ksqrt((rhor^(3))/(S))`

Explanation

`T=k(rho)^(a)(r)^(b)(S)^(c) " "[krarr "Proposnality constant"]`
where `rho="density"rArr[rho]=ML^(-3)`
`r="radious" rArr [r]=L`
`s="surface tension" rArr[s]=MT^(-2)`
`rArr [T]=k[ML^(-3)]^(a)[L]^(b)[MT^(-2)]^(c)`
`T=kM^(a+c)L^(-3a+b)T^(-2c)`
`rArr a+c=-,-3a+b=0,-2c=1rArrc=-(1)/(2)`
`a=(1)/(2), b=(3)/(2)`
`T=(k(rho)^(1/2)(r)^(3/2))/((s)^(1/2))=ksqrt((rhor^(3))/(s))`