A) \[\sqrt{\left( \frac{3k}{m} \right)h}\]
B) \[\frac{h}{2}\sqrt{\frac{3k}{m}}\]
C) \[\frac{h}{4}\sqrt{\frac{k}{m}}\]
D) \[\frac{5h}{4}\sqrt{\frac{3k}{2m}}\]
Correct Answer: C
Solution :
Consider the situational diagram Here, \[\theta =37{}^\circ ,\]\[l=h=\]natural length of spring Also, let the velocity be v. From the diagram \[\cos \,37{}^\circ =\frac{BC}{AC}\Rightarrow \frac{4}{5}=0.8=\frac{h}{h+x}\] \[\therefore \] \[AC=h+x=\frac{5h}{4}\Rightarrow x=\frac{h}{4}\] Applying work-energy theorem, \[\frac{1}{2}k\,{{x}^{2}}=\frac{1}{2}m{{v}^{2}}\Rightarrow v=x\sqrt{\frac{k}{m}}\] \[\Rightarrow \] \[v=\frac{h}{4}\sqrt{\frac{k}{m}}\]You need to login to perform this action.
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