Question

Two particles $A$ and $B$ of mass $m$ each, are joined by a rigid massless rod of length $\ell$. A particle $p$ mass $m$, moving with a speed $u$ normal to$AB$, strikes $A$ and strikes to it. The centre of mass of the ${}^{\prime }A+B+P^{\prime }$ system is $C$. Immediately after the impact

• A. $AC=\ell /3$
• B. The angular momentum of the ${}^{\prime }A+B+P^{\prime }$ system about $C$ is $mu\ell /3$
• C. The moment of inertia of the ${}^{\prime }A+B+P^{\prime }$ system about $C$ is ${2m\ell }^2$
• D. The angular velocity of the ${}^{\prime }A+B+P^{\prime }$ system is $u/2\ell$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $AC=\ell /3$
B The angular momentum of the ${}^{\prime }A+B+P^{\prime }$ system about $C$ is $mu\ell /3$
D The angular velocity of the ${}^{\prime }A+B+P^{\prime }$ system is $u/2\ell$

$\begin{array}{c}AC=\frac{m\left(l\right)}{3m}=\frac{1}{3}\\ \therefore option\left(A\right)\\ also,theangularmomentumofsystemaboutC=\frac{m4l}{3}\\ \therefore option\left(B\right)\\ also,L_i=L_f\\ \Rightarrow \frac{mul}{3}=\left[2m{\left(\frac{l}{3}\right)}^2+m{\left(\frac{2l}{3}\right)}^2\right]w\\ \Rightarrow w=\frac{u}{2l}\\ \therefore option\left(D\right)\end{array}$

Hence,

option $\left(A\right)$ $\left(B\right)$ and $\left(D\right)$ is correct answer.