Question

A solid cylinder of mass 2 Kg and radius 0.2 m is rotating about its own axis without friction with angular velocity 3 rad/s. A particle of mass 0.5 Kg and moving with a velocity of 5m/s strikes the cylinder and sticks to it as shown in. The energy of the system in the beginning is

• A. 6.43 J
• B. 2.43 J
• C. 3.43 J
• D. 8.3 J

Answer 1

Answer: (A)

6.43 J

Energy in the beginning should be $\frac{1}{2}I{\omega }^2$ for cylinder and $\frac{1}{2}m{v}^2$ for the particle.
or
$\frac{1}{2}\left(\frac{M{R}^2}{2}\right){\omega }^2+\frac{1}{2}m{v}^2=\frac{1}{2}\left(\frac{2\times 0.04}{2}\right)3^2+\frac{1}{2}0.5\times 5^2=0.18+6.25=6.43J$