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Q.

A disc of mass 100g and radius 10cm has a projection on its circumference. The mass of projection is negligible. A 20g bit of putty moving tangentially to the disc with velocity 5 ms^-1 strikes the projection and sticks to it. The angular velocity with which disc rotates is

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a

14.29 rad s^-1

b

9.82 rad s^-1

c

17.3 rad s^-1

d

12.4 rad s^-1

answer is C.

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Detailed Solution

$\begin{array}{l} mvR = (I_{disc} + I_{putty}) ω \\ mvR = (\frac{{MR}^{2}}{2} + {mR}^{2}) ω \\ mv = (\frac{M}{2} R + mR) ω \\ (20) (500) = [\frac{100}{2} (10) + 20 (10)] ω \\ 10000 = (500 + 200) ω \\ ω = \frac{100}{7} = 14 .29 rad S^{- 1} \end{array}$

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