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## Homework Statement

Four uniform rods, each of mass m and length 2L are joined rigidly to form a square frame ABCD of side 2L. The frame is placed with all four sides at rest on a smooth horizontal table. An inextensible string has one end attached to the corner A. A particle of mass 4m is tied to the other end of the string. The particle, initially at A, is projected with speed u in the direction DA. Given that the speed of the particle immediately after the string becomes taut is V, show that the initial angular speed of the square frame about an axis through its centre of gravity perpendicular to the plane of the frame is w where w=(2V-u)/L. Show that V=(7u)/11, and that immediately after the string becomes taut the kinetic energy of the particle and the frame is (14mu^2)/11.

## Homework Equations

Momentum conservation.

Impulsive moment = change in angular momentum.

Moment of inertia of a rod of mass m and length 2L about an axis through its centre = (1/3)mL^2.

Parallel axis theorem.

## The Attempt at a Solution

I've tried doing with angular momentum, linear momentum, energy conservation but I can't seem to get the right answer. Please help!!!

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