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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 tangential to the disc with a velocity of 5 ms^-1 strikes the projection and sticks to it. The angular velocity of disc is

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17.3 rads^-1

14.29 rads^-1

12.4 rads^-1

9.82 rads^-1

answer is A.

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Detailed Solution

Applying conservation of angular moment
L_i =L_f ; for disc put of system
$Mvr = (I_{disc} + {Mr}^{2}) ω$

$MvR = (\frac{{mR}^{2}}{2} + {MR}^{2}) ω$

$ω = \frac{MvR}{(\frac{{mR}^{2}}{2} + {MR}^{2})}$

$ω = \frac{20 \times 5 \times 10}{\frac{100 \times 10^{2}}{2} + 20 \times 10^{2}} = 14.29 rad / s$

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