A) 14 cycles/min
B) 10 cycles/min
C) 2.25 cycles/min
D) 7 cycles/min
Correct Answer: D
Solution :
Tension in the string should be equal to centripetal force \[T=\frac{m{{v}^{2}}}{r},\] where, \[m=\]mass of body \[r=\]radius of circular path \[v=\]linear velocity of body m and r are constant. Hence, \[v\propto \sqrt{T}\] \[\therefore \] \[\frac{{{v}_{2}}}{{{v}_{1}}}={{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{1/2}}={{\left( \frac{2{{T}_{1}}}{{{T}_{1}}} \right)}^{1/2}}\] \[{{v}_{2}}=\sqrt{2}{{v}_{1}}=\sqrt{2}\times 5\] \[=5\times 1.4=7\]cycles/min
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