A) \[\frac{9}{16}\]
B) \[\frac{4}{5}\]
C) \[\frac{25}{16}\]
D) \[\frac{5}{4}\]
Correct Answer: A
Solution :
[a] Time period of spring Case I: \[T=2\pi \sqrt{\frac{M}{K}}\] Squaring both sides \[{{T}^{2}}=4{{\pi }^{2}}\frac{M}{K}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,......(1)\] Case 2: When mass increased by m time period \[\frac{5T}{4}\] \[\frac{5T}{4}=2\pi \sqrt{\frac{M+m}{K}}\] Squaring both sides \[\frac{25{{T}^{2}}}{16}=4{{\pi }^{2}}\frac{M+m}{K}\,\,\,\,\,\,\,\,\,\,\,\,.....(2)\] From 1 and 2 \[\frac{16}{25}=\frac{M}{M+m}\Rightarrow 16M+16m=25M\] \[16m=9M\] \[\frac{m}{M}=\frac{9}{16}\]
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