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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» <html><body><p></p>Solution :When the string beomes taut , both particles move with equal velocity component v in the <a href="https://interviewquestions.tuteehub.com/tag/directon-2584492" style="font-weight:bold;" target="_blank" title="Click to know more about DIRECTON">DIRECTON</a> AB.. Perpendicular to AB. there is no impulse on either particle, velocity components in this direction are therefore <a href="https://interviewquestions.tuteehub.com/tag/unchanged-2316761" style="font-weight:bold;" target="_blank" title="Click to know more about UNCHANGED">UNCHANGED</a>. <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/AKS_ELT_AI_PHY_XI_V01_B_C04_SLV_030_S01.png" width="80%"/> <br/> Using conservation of momentum in the direction `AB.. 0 +m u sin <a href="https://interviewquestions.tuteehub.com/tag/60-328817" style="font-weight:bold;" target="_blank" title="Click to know more about 60">60</a>^(@) = mv + mv` <br/> (or) `v = (sqrt3)/(4) u` therefore, just after the jerk <br/> (i) Velocity of mass `A = (sqrt3)/(4) u` along AB.<br/> (<a href="https://interviewquestions.tuteehub.com/tag/ii-1036832" style="font-weight:bold;" target="_blank" title="Click to know more about II">II</a>) Velocity of mass `B = <a href="https://interviewquestions.tuteehub.com/tag/sqrt-1223129" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT">SQRT</a> (( u cos 60 ^(@) ) ^(2) + (( sqrt3)/( 4) u )^(2)) = (sqrt7)/(4) u` <br/> in a direction inclined to AB. at an ange `tan ^(-1) (( u cos 60 ^(@) )/(v)) , i.e., at tan ^(-1) ((2)/(sqrt3)) `<br/> The magnitude of impulsive tension (J) can be calculated by considering the change of in momentum of one of the particles. <br/> For the mass A, in the direction `AB. , J = mv - 0 (or) J = (sqrt3)/(4) m u`</body></html>


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