Time period of a spring of negligible mass, with a mass M hanging from it, is T. The time period chnages to `(5T)/3` on attaching an additional mass m to it. Find out the value of `m/M`.

Explanation

From the formula `T=2pisqrt(m/k)`, we get, `T/(T.)=sqrt(m/(m.))`
For the given cases,
`T/((5T)/3)=sqrt(M/(M+m))or,3/5=sqrt(M/(M+m))`
or, `(M+m)/M=25/9or,1+m/M=25/9`
`therefore" "m/M=25/9-1=16/9`.