A) 2 kg
B) 1 kg
C) 1.6kg
D) 2.6 kg
Correct Answer: C
Solution :
Time period of vibration \[T=2\pi \sqrt{\frac{m}{k}}\] \[\Rightarrow \] \[T\propto \sqrt{m}\] So, for two conditions \[\frac{{{T}_{2}}}{{{T}_{1}}}=\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}\] or \[\frac{{{T}_{2}}}{{{T}_{1}}}=\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}\] or \[\sqrt{\frac{9}{4}}=\frac{m+2}{m}\] \[\Rightarrow \] \[m=1.6kg\]
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