A) 18
B) 12
C) 36
D) 48
Correct Answer: B
Solution :
From the relation of angular velocity \[{{\omega }^{2}}=\omega _{0}^{2}+2\alpha s\] \[{{\left( \frac{{{\omega }_{0}}}{2} \right)}^{2}}=\omega _{0}^{2}+2\alpha \times 72\pi \] \[\alpha =-\frac{3}{4}\frac{\omega _{0}^{2}}{144\pi }\] Let it complete n rotation more before coming to rest \[0={{\left( \frac{{{\omega }_{0}}}{2} \right)}^{2}}-2\times \frac{3}{4}\times \frac{\omega _{0}^{2}}{144\pi }\times n\times 2\pi \] \[\frac{\omega _{0}^{2}}{4}=2\times \frac{3}{4}\frac{\omega _{0}^{2}}{144\pi }n\times 2\pi \] Hence, \[n=12\]
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