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.

Two particles A and B of equal mass m each are attached by a string of

1.	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.
Answer» Solution :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`