Two particles of same mass m are connected by an ideal string of length l. Consider system to be present in free space and string is just taut. Now an impulse is imparted to particle A in direction perpendicular to string, due to this instantaneously it starts moving with speed u. In subsequent motion in the frame of reference of particle A, the particle B performs periodic motion with time period T

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Magnitude of tension in string remains constant

T=2πlu

T=πlu

In a general interval of time t =t to t = t + T the particle B travels a distance equal to 4l

answer is A.

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Detailed Solution

Both the particles are performing circular motion in C-frame with angular speed ω=u/l⇒2πT=u/l⇒T=2πlu, the CM moves uniformly with velocity Vcom=m1u1+m1u2m1+m2=mu+m(0)m+m=u/2rcom=m1r1+m1r2m1+m2=ml+m(0)m+m=l/2. Radius of circular paths is r= rcom=l/2.Tension remains constant equal to =mrω2=ml2ul2=mu22l. In G – frame trajectory of both the particles is cycloid, which is identical to trajectory of a particle on circumference of purely rolling ring of radius R which travels a distance 8R in one time period.distance=8R=8l2=4l

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