6 Fig. 6.1 shows a light rod ABC , of length 60 cm , where B is the midpoint of AC . Particles of masses \(3.5 \mathrm {~kg} , 1.4 \mathrm {~kg}\) and 2.1 kg are attached to \(\mathrm { A } , \mathrm { B }\) and C respectively.
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\caption{Fig. 6.1}
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The centre of mass is located at a point G along the rod.
- Determine the distance AG .
Two light inextensible strings, each of length 40 cm , are attached to the rod, one at A , the other at C. The other ends of these strings are attached to a fixed point D. The rod is allowed to hang in equilibrium.
- Determine the angle AD makes with the vertical.
The two strings are now replaced by a single light inextensible string of length 80 cm . One end of the string is attached to A and the other end of the string is attached to C. The string passes over a smooth peg fixed at D. The rod hangs in equilibrium, but is not vertical, as shown in Fig. 6.2.
Fig. 6.2
- Explain why angle ADG and angle CDG must be equal.
- Determine the tension in the string.