A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes simple harmonic oscillation with a time period T. If the mass is increased by m, the time period becomes `((5)/(4)T)`. The ratio of `(m)/(M)` is...........

Options

A. `(9)/(16)`
B. `(25)/(16)`
C. `(4)/(5)`
D. `(5)/(4)`

Answer

A

Explanation

`T= 2pi sqrt((m)/(k)) implies m propto T^(2)`
`therefore (m_2)/(m_1)= (T_(2)^(2))/(T_(1)^(2))`
`implies (M+m)/(M)= (((5)/(4)T)/(T))^(2) implies (m)/(M)= (9)/(16)`.