A) 0.09 m
B) 0.3 m
C) 0.03 m
D) 0.9 m
Correct Answer: B
Solution :
Time period of spring is given by \[T=2\pi \sqrt{\left( \frac{m}{k} \right)}\] \[\Rightarrow \] \[\omega =\frac{2\pi }{T}=\sqrt{\left( \frac{k}{m} \right)}\] \[\therefore \] \[\omega =\sqrt{\left( \frac{10}{10} \right)}=1\] Velocity of mass at displacement\[x\] \[u=\omega \sqrt{{{a}^{2}}-{{y}^{2}}}\] \[\Rightarrow \] \[{{y}^{2}}={{a}^{2}}=\frac{{{u}^{2}}}{{{\omega }^{2}}}\] \[={{(50)}^{2}}-\frac{{{(40)}^{2}}}{{{1}^{2}}}\] \[={{(50)}^{2}}-{{(40)}^{2}}\] \[=(50+40)(50-40)=900\] \[\therefore \] \[y=30\,cm=0.3\,m\]
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