A) \[u=\frac{\pi F_{0}^{2}}{2m}\]
B) \[u=\frac{\pi {{T}^{2}}}{8m}\]
C) \[u=\frac{\pi {{F}_{0}}T}{4m}\]
D) \[u=\frac{{{F}_{0}}T}{2m}\]
Correct Answer: C
Solution :
Initially particle was at rest. By the application of force its momentum increases. Final momentum of the particle \[=\]Area of F - t graph Þ \[mu=\]Area of semicircle \[mu=\frac{\pi \ {{r}^{2}}}{2}\]\[=\frac{\pi \ {{r}_{1}}{{r}_{2}}}{2}\]\[=\frac{\pi \ ({{F}_{0}})\ (T/2)}{2}\]Þ\[u=\frac{\pi \ {{F}_{0}}T}{4m}\]
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