A) \[0.1556\text{ }sec\]
B) \[0.1456\text{ }sec\]
C) \[0.1356\text{ }sec\]
D) \[0.1256\text{ }sec.\]
Correct Answer: D
Solution :
As the platform is executing SHM, its time period will be minimum when it has the maximum acceleration. We know that in SHM, the maximum acceleration is given by \[{{a}_{\max }}={{\omega }^{2}}A\] Now if the body is not to be detached from the platform, \[{{a}_{\max }}\] should be less than the acceleration due to gravity. In the limiting case, \[{{a}_{\max }}=g\] \[\Rightarrow \] \[{{\omega }^{2}}A=g\] \[\Rightarrow \,\,\frac{4{{\pi }^{2}}A}{{{T}^{2}}}=g\] \[\Rightarrow \] \[T=2\pi \sqrt{\frac{A}{g}}=2\pi \times \sqrt{\frac{3.92\times {{10}^{-4}}}{9.8}}\] \[\therefore \] \[{{T}_{\min }}=0.1256\sec .\]You need to login to perform this action.
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