An object of mass 8   kg is hanging from one end of a uniform rod C D of mass 2   kg and length 1…

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)

 

  1. 240 N
  2. 90 N
  3. 300 N
  4. 30 N

Solution

Let T be the tension in cable.

Since the system is at equilibrium, the net torque, about an axis perpendicular to the plane and passing through the point of contact of the rod and the wall, is zero. Therefore, torque about point C

T sin30°× 60=mg×50+8g×100

T2×60=20×50+80×100

3T=100+800

300 N.

Asked in: JEE Main 2023 (25 Jan Shift 1)

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