Question

A uniform rod of mass 300 g and length 50 cm rotates at a uniform angular speed of 2 rad/s about an axis perpendicular to the rod through an end. The angular momentum of the rod about the axis of rotation, the speed of the centre of the rod and its kinetic energy respectively are_______, _______ and _______.

• A. $0.05kg-m^2/s,0.5cm/s,0.05J$
• B. $0.5kg-m^2/s,0.5m/s,0.5J$
• C. $0.05kg-m^2/s,50cm/s,0.05J$
• D. $0.05kg-m^2/s,50m/s,5J$

Answer 1

The correct option is C $0.05kg-m^2/s,50cm/s,0.05J$

$I=\frac{m{l}^2}{3}\text{(about one end)}$

$=\frac{0.3\times {0.5}^2}{3}=0.025kg-m^2$

$\text{Angular momentum}=I\times \omega =0.025\times 2$

$=0.05kg-m^2/s$

$\text{Speed of centre of rod}=\omega \times \frac{L}{2}=0.5m/s$

$\text{Kinetic energy}=\frac{1}{2}\times I\times {\omega }^2=0.05J$