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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 simple harmonic oscillations with a time period T. If the mass is increased by m then the time period becomes $(\frac{5}{4} T)$ . The ratio of $\frac{m}{M}$ is

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a

4/5

b

25/16

c

9/16

d

5/4

answer is A.

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Detailed Solution

$T = 2 π \sqrt{\frac{m}{K}} \Rightarrow m α T^{2} \Rightarrow \frac{m_{2}}{m_{1}} = \frac{T_{2}^{2}}{T_{1}^{2}}$

$\Rightarrow \frac{M + m}{M} = (\frac{\frac{5}{4} T}{T}) \Rightarrow \frac{m}{M} = \frac{9}{16}$

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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 oscillations with a time period T. If the mass is increased by m then the time period becomes 54T. The ratio of mM is