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NEET PHYSICSRotational motionMedium

Question

A uniform rod of length 200 cm200 \text{ cm} and mass 500 g500 \text{ g} is balanced on a wedge placed at 40 cm40 \text{ cm} mark. A mass of 2 kg2 \text{ kg} is suspended from the rod at 20 cm20 \text{ cm} and another unknown mass mm is suspended from the rod at 160 cm160 \text{ cm} mark as shown in the figure. What would be the value of mm such that the rod is in equilibrium? (Take g=10 m/s2g=10 \text{ m/s}^2)

A

16 kg\frac{1}{6} \text{ kg}

B

112 kg\frac{1}{12} \text{ kg}

C

12 kg\frac{1}{2} \text{ kg}

D

13 kg\frac{1}{3} \text{ kg}

Step-by-Step Solution

Let us consider the torques about the wedge placed at the 40 cm40 \text{ cm} mark. Mass of the rod, M=500 g=0.5 kgM = 500 \text{ g} = 0.5 \text{ kg}. Since the rod is uniform, its weight acts at its centre of gravity, which is at the 100 cm100 \text{ cm} mark. Distance of the 2 kg2 \text{ kg} mass from the wedge = 40 cm−20 cm=20 cm=0.2 m40 \text{ cm} - 20 \text{ cm} = 20 \text{ cm} = 0.2 \text{ m}. Distance of the centre of gravity of the rod from the wedge = 100 cm−40 cm=60 cm=0.6 m100 \text{ cm} - 40 \text{ cm} = 60 \text{ cm} = 0.6 \text{ m}. Distance of the unknown mass mm from the wedge = 160 cm−40 cm=120 cm=1.2 m160 \text{ cm} - 40 \text{ cm} = 120 \text{ cm} = 1.2 \text{ m}. For the rod to be in rotational equilibrium, the net torque about the wedge must be zero. By the principle of moments, the sum of anticlockwise moments equals the sum of clockwise moments. Anticlockwise moment = Moment due to 2 kg2 \text{ kg} mass = 2×g×0.22 \times g \times 0.2 Clockwise moment = Moment due to rod's weight + Moment due to mass mm = 0.5×g×0.6+m×g×1.20.5 \times g \times 0.6 + m \times g \times 1.2 Equating the moments: 2×g×0.2=0.5×g×0.6+m×g×1.22 \times g \times 0.2 = 0.5 \times g \times 0.6 + m \times g \times 1.2 0.4=0.3+1.2m0.4 = 0.3 + 1.2m 0.1=1.2m0.1 = 1.2m m=0.11.2=112 kgm = \frac{0.1}{1.2} = \frac{1}{12} \text{ kg}.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from Rotational motion. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSRotational motionuniformlengthbalancedplacedsuspended

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