2. The masses of two particles \(A\) and \(B\) are 0.5 kg and \(m \mathrm {~kg}\) respectively. The particles are moving on a smooth horizontal table in opposite directions and collide directly. Immediately before the collision the speed of \(A\) is \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of \(B\) is \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). In the collision, the magnitude of the impulse exerted by \(B\) on \(A\) is 3.6 Ns. As a result of the collision the direction of motion of \(A\) is reversed.
- Find the speed of \(A\) immediately after the collision.
The speed of \(B\) immediately after the collision is \(1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- Find the two possible values of \(m\).
\section*{3.}
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\caption{Figure 1}
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A uniform rod \(A B\) has length 100 cm . Two light pans are suspended, one from each end of the rod, by two strings which are assumed to be light and inextensible. The system forms a balance with the rod resting horizontally on a smooth pivot, as shown in Fig. 1.
A particle of weight 16 N is placed in the pan at \(A\) and a particle of weight 5 N is placed in the pan at \(B\). The rod rests horizontally in equilibrium when the pivot is at the point \(C\) on the rod, where \(A C = 30 \mathrm {~cm}\). - Find the weight of the rod.
(3)
The particle in the pan at \(A\) is replaced by a particle of weight 3.5 N . The particle of weight 5 N remains in the pan at \(B\). The rod now rests horizontally in equilibrium when the pivot is moved to the point \(D\). - Find the distance \(A D\).
- Explain briefly where the assumption that the strings are light has been used in your answer to part (a).