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NEET 2026
Exam
NEET
Year
2026
Subject
Physics
Chapter
Chapter

NEET 2026 · Physics · Chapter

A uniform horizontal beam of mass 6 kg and length L is hinged to a...

A uniform horizontal beam of mass 6 kg and length L is hinged to a vertical wall at one end. The other end is supported
A uniform horizontal beam of mass 6 kg6\text{ kg} and length LL is hinged to a vertical wall at one end. The other end is supported by a light inextensible wire attached to the same wall, making an angle of 30∘30^{\circ} with the beam. A block of mass 9 kg9\text{ kg} is suspended from the free end of the beam. The horizontal component of the reaction force exerted by the hinge on the beam is (Take g=10 m/s2g = 10\text{ m/s}^2)

Options

  1. A903 N90\sqrt{3}\text{ N}
  2. B120 N120\text{ N}
  3. C1203 N120\sqrt{3}\text{ N}
  4. D1503 N150\sqrt{3}\text{ N}

Correct answer

C. 1203 N120\sqrt{3}\text{ N}

Step-by-step solution

Let the length of the beam be LL.

Taking torque about the hinge to be zero for rotational equilibrium:

Tsin⁡30∘×L=60×L2+90×LT \sin 30^{\circ} \times L = 60 \times \dfrac{L}{2} + 90 \times L

T×12=30+90T \times \dfrac{1}{2} = 30 + 90

T=240 NT = 240\text{ N}

For horizontal equilibrium, the net force in the horizontal direction is zero. The horizontal component of the hinge reaction RxR_x balances the horizontal component of the tension:

Rx=Tcos⁡30∘R_x = T \cos 30^{\circ}

Rx=240×32=1203 NR_x = 240 \times \dfrac{\sqrt{3}}{2} = 120\sqrt{3}\text{ N}

Answer: 1203 N120\sqrt{3}\text{ N}
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