A) \[x=\frac{1}{v}\,\sqrt{\frac{m}{k}}\]
B) \[x=\,\sqrt{\frac{m}{k}}\]
C) \[x=\,V\,\sqrt{\frac{m}{k}}\]
D) \[x=\,\,\sqrt{\frac{mv}{k}}\]
Correct Answer: C
Solution :
Time period \[T=2\pi \sqrt{\frac{m}{k}}\]and\[\omega =\frac{2\pi }{T}=\sqrt{\frac{k}{m}}\] When spring is at its natural length, the velocity of block is maximum. So, \[v=r\omega \] According to question \[\operatorname{r}\,\,=\,\,x,\,\,So\,\,v=x\omega \] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,x=\frac{v}{\omega }=v\sqrt{\frac{m}{k}}\]You need to login to perform this action.
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