Two particles A and B each of mass m are attached by a light inextensible string of length 2l. The whole system lies on a smooth horizontal table with B initially at a distance l from A. The particle at end B is projected across the table with speed u perpendicular to AB. Velocity of ball A just after the string is taut is u√x/4. The value of x is ...
Physics · Mixed Chapter
JEE Mains

Question

Two particles A and B each of mass m are attached by a light inextensible string of length 2l. The whole system lies on a smooth horizontal table with B initially at a distance l from A. The particle at end B is projected across the table with speed u perpendicular to AB. Velocity of ball A just after the string is taut is u√x/4. The value of x is ...

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Let the initial separation be l and final taut string length 2l. B has moved a horizontal distance √[(2l)²−l²]=√3l when the string becomes taut. Step 2: The taut string makes angle 30° with B's horizontal velocity. The velocity component along the string just before it tightens is u cos30°=(√3/2)u. Step 3: During the instant of tightening, equal masses share the string-direction component of momentum. A acquires speed (1/2)(√3/2)u=(√3/4)u. Step 4: Comparing with u√x/4 gives x=3.