An object of mass 8 kg is hanging from one end of a uniform rod CD of… | JEE Main 2023 (25 Jan, Shift 1)

Q17JEE Main 2023 · 25 JAN · SHIFT 1Medium

Torque, Couple & Equilibrium of Rigid Bodies

An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg and length 1 m pivoted at its end C on a vertical wall as shown in figure. It is supported by a cable AB such that the system is in equilibrium. The tension in the cable is (Take g = 10 m/s $2$ )

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Answer: (d)

Take torques about the pivot C. The cable at B ( $CB = 0.6$ m) makes $30^\circ$ with the rod, so its perpendicular part is $T\sin 30^\circ$ .
Rod weight $20$ N acts at $0.5$ m; hanging weight $80$ N acts at $1$ m.
$T \sin 30^\circ \times 0.6 = 20 \times 0.5 + 80 \times 1 = 90$
$0.3\,T = 90 \Rightarrow T = 300$ N
So the answer is (d) 300 N.

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Torque, Couple & Equilibrium of Rigid Bodies question from JEE Main 2023 (25 Jan, Shift 1)

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