Question

A rod of mass m and length I is lying along the y - axis such that one of its ends is a the origin. Suddenly an impulse is given to the rod such that immediately after the impulse, the end of the origin has a velocity $v_0\hat{i}$ and the other end has a velocity $2v_0\hat{i}$. The magnitude of angular momentum of the rod about the origin at this instant is

• A. $\frac{2}{3}m{v}_{0}l$
• B. $\frac{3}{2}m{v}_{0}l$
• C. $\frac{6}{5}m{v}_{0}l$
• D. $\frac{5}{6}m{v}_{0}l$

Answer 1

The correct option is A $\frac{2}{3}m{v}_{0}l$

let the impulse acts at a point distance $r_1$ from the origin$.$

Therefore the distance of second and from the point where impulse is given by$:$

$\left(l-r_1\right).$

therefore$,$ $f_1{t}_1{r}_1=f_2{t}_2\left(l-r_1\right)$

$or,m\times \frac{v_0}{t_1}\times t_1{r}_1=m\times \frac{2v_0}{t_2}\times t_2\left(l-r_1\right)$

$or,r_1=2l-2r_1$

$or,r_1=\frac{2l}{3}$

therefore the angular momentum of the rod about origin is given by the angular momentum of the point of impulse from the origin $i.e.,$

$L=m{v}_0,r_1=\frac{2m{v}_{0}l}{3}$

Hence,

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