1. Tardigrade
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  4. 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 SHM of time period T. If the mass is increased by m, the time period becomes text5T/3, then the ratio of (m/M) is

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Q. 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 SHM of time period T. If the mass is increased by m, the time period becomes $ \text{5T/3,} $ then the ratio of $ \frac{m}{M} $ is

Rajasthan PMTRajasthan PMT 2008Oscillations

Solution:

$ T=2\pi \sqrt{\frac{M}{k}} $ $ T=2\pi \sqrt{\frac{M+m}{k}} $ $ \Rightarrow $ $ \frac{5T}{3}=2\pi \sqrt{\frac{M+m}{k}} $ Dividing Eq. (i) by Eq (ii), we have $ \frac{3}{5}=\sqrt{\frac{M}{M+m}} $ $ \frac{9}{25}=\frac{M}{M+m} $ $ \Rightarrow $ $ 9M+9m=25M $ $ \Rightarrow $ $ 16M=9m $ $ \frac{m}{M}=\frac{16}{9} $