Question

A disc of mass 100 g and radius 10 cm has a projection on its circumference. The mass of projection is negligible. A 20 g bit of putty moving tangential to the disc with a velocity of 5$m{s}^{-1}$ strikes the projection and strickes to it. the angular velocity of disc is

• A. 14.29 $rad{s}^{-1}$
• B. 17.3 $rad{s}^{-1}$
• C. 12.4 $rad{s}^{-1}$
• D. 9.82 $rad{s}^{-1}$

Answer 1

Answer: (A)

14.29 $rad{s}^{-1}$

In this case the angular momentum of bit of putty about the axis of rotation is equal to the angular momentum of system of disc and bit of putty about the axis of rotation.

Given,

Mass of putty, $M=20g$

Mass of disc, $m=100g$

Radius of the disc, $R=10cm$

Velocity, $v=5m/s$

We have the equation

$MvR=(\frac{m{R}^2}{2}+M{R}^2)\omega$

$w=\frac{MvR}{(\frac{m{R}^2}{2}+M{R}^2)}$

Substituting the values, we get

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