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Rotational Motion question

2024 · 27 Jan · Shift 2 · Q65
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  5. /2024 · 27 Jan · Shift 2 · Q65

Rotational Motion question

2024 · 27 Jan · Shift 2 · Q65

JEE MainPhysicsRotational MotionMCQ+4 / −1
A heavy iron bar of weight 12 kg12 \mathrm{~kg}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∘60^{\circ}60∘ with the horizontal, the weight experienced by the man is :
  1. A
    3 kg3 \mathrm{~kg}3 kg
  2. B
    6 kg6 \mathrm{~kg}6 kg
  3. C
    63 kg6 \sqrt{3} \mathrm{~kg}63​ kg
  4. D
    12 kg12 \mathrm{~kg}12 kg
View written solutionFree

Correct answer: B: $6 \MATHRM{~KG}$

  1. Understand the setup

A uniform heavy iron bar has:

  • one end on the ground,
  • the other end on the man's shoulder,
  • inclination with horizontal =60∘=60^\circ=60∘,
  • weight of bar =12 kg-wt=12\,\text{kg-wt}=12kg-wt.

We need the load supported by the man.

  1. Forces acting on the bar

Since the bar is uniform, its weight acts at its midpoint.

Let:

  • lower end on ground be point AAA,
  • upper end on shoulder be point BBB,
  • length of rod be LLL.

For vertical equilibrium:

  • upward reaction from ground at AAA = RAR_ARA​,
  • upward force from man's shoulder at BBB = RBR_BRB​,
  • downward weight at midpoint = 121212 kg-wt.

So, RA+RB=12R_A + R_B = 12RA​+RB​=12

  1. Take moments about the ground end AAA

This eliminates RAR_ARA​.

  • Weight acts at midpoint, whose horizontal distance from AAA is L2cos⁡60∘\frac{L}{2}\cos 60^\circ2L​cos60∘
  • Force by man acts at BBB, whose horizontal distance from AAA is Lcos⁡60∘L\cos 60^\circLcos60∘

Both forces are vertical, so their moment arms are these horizontal distances.

Balancing moments about AAA: RB (Lcos⁡60∘)=12(L2cos⁡60∘)R_B\,(L\cos 60^\circ)=12\left(\frac{L}{2}\cos 60^\circ\right)RB​(Lcos60∘)=12(2L​cos60∘)

Cancel Lcos⁡60∘L\cos 60^\circLcos60∘ from both sides: RB=12⋅12=6R_B=12\cdot \frac{1}{2}=6RB​=12⋅21​=6

  1. Interpretation

Thus the man supports a load of 6 kg-wt6\,\text{kg-wt}6kg-wt

  1. Check options
  • A: 333 kg ✗
  • B: 666 kg ✓
  • C: 636\sqrt{3}63​ kg ✗
  • D: 121212 kg ✗

Therefore, the correct option is B.

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