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...........

A mass M is suspended from a spring of negligible mass. The spring is

1.	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...........
Answer» `(9)/(16)` `(25)/(16)` `(4)/(5)` `(5)/(4)` Solution :`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)`.