A) \[2\sqrt{\frac{p}{k}}\]
B) \[\sqrt{\frac{2k}{p}}\]
C) \[\sqrt{\frac{2p}{k}}\]
D) \[2\sqrt{\frac{k}{p}}\]
Correct Answer: A
Solution :
| [a]: As\[F=\frac{dp}{dt}\]or\[kt\,dt=dp\] |
| Integrating both sides, |
| \[k\int\limits_{0}^{T}{t}dt=\int_{p}^{3p}{dp}\] |
| \[\frac{k{{T}^{2}}}{2}=[3p-p]=2p\] |
| \[\therefore \]\[T=2\sqrt{\frac{p}{k}}\] |
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