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two particles A and B each of mass m are attached by a liight inextensible string of length 2l.the whole system lies on a smooth horizontal table with B initially at adistance l from A.the particle at end B is projected across the table with speed u perpendicular to AB.find the speed of A just after string becomes taut.
Resolve velocity of B along and perpendicular to AB. It is u/2 and u*(sqrt(3))/2.For direction perpendicular to AB, apply conservation of linear momentum to get velocity of A = u/4. Apply conservation of angular momentum to get velocity of A = -u/4. So, velocity of A perpendicular to AB = 0.For direction along AB, apply conservation of linear momentum to get velocity of A = u*(sqrt(3))/4.Which is the required answer
Resolve velocity of B along and perpendicular to AB. It is u/2 and u*(sqrt(3))/2.
For direction perpendicular to AB, apply conservation of linear momentum to get velocity of A = u/4. Apply conservation of angular momentum to get velocity of A = -u/4. So, velocity of A perpendicular to AB = 0.
For direction along AB, apply conservation of linear momentum to get velocity of A = u*(sqrt(3))/4.
Which is the required answer
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