A) \[\frac{1}{6}\pi \sqrt{\frac{k}{m}}\]
B) \[\sqrt{\frac{k}{m}}\]
C) \[\frac{2\pi }{3}\sqrt{\frac{m}{k}}\]
D) \[\frac{\pi }{4}\sqrt{\frac{k}{m}}\]
Correct Answer: C
Solution :
The total time from A to C \[{{t}_{Ac}}={{t}_{AB}}+{{t}_{BC}}\] \[=(T/4)+{{t}_{BC}}\] where T = time period of oscillation of spring mass system \[{{t}_{BC}}\] can be obtained from, \[BC=AB\sin (2\pi /T)\,{{t}_{BC}}\] Putting \[\frac{BC}{AB}=\frac{1}{2}\] we obtain \[{{t}_{BC}}=\frac{T}{12}\] Þ \[{{t}_{AC}}=\frac{T}{4}+\frac{T}{12}=\frac{2\pi }{3}\sqrt{\frac{m}{k}}\].You need to login to perform this action.
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