Question

Consider a body shown in the figure below, consisting of two identical balls, each of mass 'M' connected by a light rigid rod of length 'L'. If an impulse, J = Mv is imparted to the body at one of its ends, what would be its angular velocity?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Initial angular momentum of the system about point O
= Linear momentum $\times$ Perpendicular distance of linear momentum from the axis of rotation $=Mv\left(\frac{L}{2}\right)...\left(i\right)$
Final angular momentum of the system about point $O=I_1\omega +I_2\omega =(I_1+I_2)\omega$
$=[M{\left(\frac{L}{2}\right)}^2+M{\left(\frac{L}{2}\right)}^2]\omega$ .....(ii)
Applying the law of conservation of angular momentum
$\Rightarrow Mv\left(\frac{L}{2}\right)=2M{\left(\frac{L}{2}\right)}^2\omega$ $\Rightarrow \omega =\frac{v}{L}$