Two particles A and B of equal mass m each are attached by a string of length 21 and initally placed over a smooth horizontal table in the position shown in figure Particle B is projected across the table with speed u perpendicular to AB as shown in figure. Find the velocities of the particles after the string becomes taut and the magnitude of the impulsive tension.

Explanation

When the string beomes taut , both particles move with equal velocity component v in the directon AB.. Perpendicular to AB. there is no impulse on either particle, velocity components in this direction are therefore unchanged.

Using conservation of momentum in the direction `AB.. 0 + m u sin 60^(@) = mv + mv`
(or) `v = (sqrt3)/(4) u` therefore, just after the jerk
(i) Velocity of mass `A = (sqrt3)/(4) u` along AB.
(ii) Velocity of mass `B = sqrt (( u cos 60 ^(@) ) ^(2) + (( sqrt3)/( 4) u )^(2)) = (sqrt7)/(4) u`
in a direction inclined to AB. at an ange `tan ^(-1) (( u cos 60 ^(@) )/(v)) , i.e., at tan ^(-1) ((2)/(sqrt3)) `
The magnitude of impulsive tension (J) can be calculated by considering the change of in momentum of one of the particles.
For the mass A, in the direction `AB. , J = mv - 0 (or) J = (sqrt3)/(4) m u`