A) \[\sqrt{\frac{4}{3}}T\]
B) \[\frac{{{3}^{2}}}{{{4}^{2}}}T\]
C) \[\frac{\sqrt{3}}{2}T\]
D) \[\frac{3}{4}T\]
Correct Answer: C
Solution :
For a body executing circular motion, centripetal force is given by \[F=mr{{\omega }^{2}}=mr{{\left( \frac{2\pi }{T} \right)}^{2}}\] ... (i) If k is force constant of string, then elastic force F = ka ... (ii) From Eqs. (i) and (ii), we get \[ka+m\,(2a)\,{{\left( \frac{2\pi }{T} \right)}^{2}}\] ... (iii) In second case New length of string = new radius of circle = 3d Stretching of string = 3a - a = 2 a Hence, elastic force = k . 2 a So, \[k\,.\,2a=m\,(3\,a)\,{{\left( \frac{2\,\pi }{T} \right)}^{2}}\] ... (iv) Dividing Eq. (iv) by Eq. (iii), we get \[2=\frac{3}{2}{{\left( \frac{T}{T} \right)}^{2}}\] \[\Rightarrow \] \[{{\left( \frac{T}{T} \right)}^{2}}=\frac{4}{3}\] \[\Rightarrow \] \[T=\frac{\sqrt{3}}{2}\,T\]You need to login to perform this action.
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