A heavy iron bar of weight 12 kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle 60∘ with the horizontal, the weight experienced by the man is :
(A)6 kg
(B)12 kg
(C)3 kg✓ Correct
(D)63kg
Answer: (C)
Solution
The rod rests on the man's shoulder as on a smooth support, so the reaction N2 it exerts there acts perpendicular to the rod itself, while the rod's weight W=120N acts vertically at its midpoint. Taking torques about the point O where the rod meets the ground, the weight's moment arm is its horizontal distance from O, 2Lcos60∘, while N2, already perpendicular to the rod, has moment arm equal to the full length L:
N2L=W(2L)cos60∘=120×2L×21
N2=30N=3kg-wt.
By Newton's third law, this is the weight the man's shoulder feels.
JEE Main · 2024 · 27 Jan 2024 · Shift 2 · Single correct option
