Question

A uniform rod of mass m and length l is at rest on smooth horizontal surface. An impulse P is applied to end B as shown in the figure. The point about which the rod can be assumed to be rotating just after the impulse is applied is

• A. at $\frac{l}{2}$ from A
• B. at $\frac{l}{3}$ from A
• C. at $\frac{l}{4}$ from A
• D. at $\frac{l}{6}$ from A

Answer 1

The correct option is B at $\frac{l}{3}$ from A

Appling impulse - momentum theorem : $V_{cm}=\frac{p}{m}$ and Angluar impulse about the center $P=\frac{1}{12}m{l}^2\omega$
$\omega =\frac{6p}{ml}$
If x be distance from centre of the rod
$\frac{p}{m}-\frac{6p}{ml}\times x=0\Rightarrow x=\frac{1}{6}$ As the velocity at the instantaneous center is zero)
So distance of the instantaneous centre of rotation from $A=\frac{1}{2}-\frac{1}{6}=\frac{1}{3}$