A rod of mass m and length l is lying along the y-axis such that one of its ends is - Physics - System Of Particles And Rotational Motion

Question

A rod of mass m and length l is lying along the y-axis such that
one of its ends is at the origin Suddenly an impulse is given to
the rod such that immediately after the impulse, the end on the
origin has a velocity voi^ and the other end
has a velocity 2vo ​i The magnitude of
angular momentum of the rod about the origin at this instant
is?
(a)2/3 mv​ol (b) 3/2 mvol (c) 5/6
mvol (d) 7/8mvol

Ved Prakash Lakhera · Accepted Answer

Let the impulse acts at a point distance r1 from the origin
Therefore the distance of second end from the point where impulse is imparted,is given by l-r1
Therefore       f1t1r1=f2t2l-r1or                   m×v0t1×t1r1=m×2v0t2×t2l-r1or                   r1=2l-2r1or                   r1=2l3Therefore 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=mv0  r1=2mv0l3Therefore correct answer is option a 23mv0l