A) \[\frac{3}{5}\]
B) \[\frac{25}{9}\]
C) \[\frac{16}{9}\]
D) \[\frac{5}{3}\]
Correct Answer: C
Solution :
The time period for the SHM, \[T=2\pi \sqrt{\frac{M}{k}}\] ... (i) and \[T'=2\pi \sqrt{\frac{M+m}{k}}\] \[\Rightarrow \] \[\frac{5T}{3}=2\pi \sqrt{\frac{M+m}{k}}\] ... (ii) Dividing Eq. (i) by Eq. (ii), we have \[\frac{3}{5}=\sqrt{\frac{M}{M+m}}\] \[\Rightarrow \] \[\frac{9}{25}=\frac{M}{M+m}\] \[\Rightarrow \] \[9M+9m=25M\] \[\Rightarrow \] \[16M=9m\] \[\therefore \] \[\frac{m}{M}=\frac{16}{9}\]You need to login to perform this action.
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