Question

A thin uniform straight rod of mass $2$ kg and length $1$ m is free to rotate about its upper end when at rest. It receives an impulsive blow of $10$ Ns at its lowest point, normal to its length as shown in figure. Find kinetic energy of the rod just after impact.

• A. 75 J
• B. 100 J
• C. 200 J
• D. none

Answer 1

The correct option is C 200 J

Angular impulse $=$ change in angular momentum

$10\times 1=I\omega -0$

$I=$ moment of inertia of rod about it upper end = $\frac{1}{12}m{L}^2+m(\frac{L}{2}{)}^2=\frac{1}{3}m{L}^2$

$\frac{1}{3}m{L}^2\omega =10$

kinetic energy will be(KE) $=\frac{1}{2}I{w}^2$

$KE=\frac{1}{2}\times \left(\frac{1}{3}m{L}^2\right)\times (\frac{30}{m{L}^2}{)}^2$

$KE=\frac{300}{2m{L}^2}$

$KE=\frac{150}{2}$

$KE=75$J