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 it starts moving with speed u instantaneously. In subsequent motion

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In a general interval of time t=t to t=t+T, the particle B travels a distance equal to 4l. (T is time period of periodic motion of one particle in frame of other)

In the frame of reference of particle A the particle B performs periodic motion with period $T = \frac{2 π l}{u}$

In the frame of reference of particle B the particle A performs periodic motion with period $T = \frac{π l}{u}$

Magnitude of tension in string remains constant.

answer is A, B, D.

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Detailed Solution

Both the particles are performing circular motion in C-frame with angular speed w=u/l, the CM moves uniformly with velocity u/2. Radius of circular path is l/2.
Tension remains constant equal to $m (\frac{l}{2}) {(\frac{u}{l})}^{2} = \frac{{mu}^{2}}{2 l}$
In Ground 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.