Question-09 A mass m is suspended from a spring of negligible mass. The spring is pulled a little and then released, so that mass executes S.H.M. of time period T. If the mass is increased by m_0, the periodic time becomes \frac{5T}{4}. The ratio \frac{m_0}{M} is
(A) \frac{3}{4}
(B) \frac{4}{3}
(C) \frac{9}{16}
(D) \frac{16}{9}
Answer : (C)
Explanation:
T'=\frac{5T}{4}\Rightarrow \frac{T'}{T}=\frac{5}{4}Here, the hanging mass performs S.H.M.
With T=2\pi\sqrt{\frac{m}{k}} and
T'=2\pi\sqrt{\frac{m+m_0}{k}}∴ \frac{T'}{T}=\sqrt{\frac{m+m_0}{k}\times\frac{k}{m}}
∴ \frac{5}{4}=\sqrt{\frac{m+m_0}{m}}
∴ \frac{m+m_0}{m}=\frac{25}{16}
∴ 9m=16m_0\Rightarrow \frac{m_0}{m}=\frac{9}{16}