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NEET PHYSICSRotational motionMedium

Question

Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D1D_1 has 2 kg2\text{ kg} mass and 0.2 m0.2\text{ m} radius and initial angular velocity of 50 rad s−150\text{ rad s}^{-1}. Disc D2D_2 has 4 kg4\text{ kg} mass, 0.1 m0.1\text{ m} radius and initial angular velocity of 200 rad s−1200\text{ rad s}^{-1}. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad s−1\text{rad s}^{-1}) of the system is

A

6060

B

100100

C

120120

D

4040

Step-by-Step Solution

Let the moments of inertia of the two discs be I1I_1 and I2I_2. For a uniform disc, I=12MR2I = \frac{1}{2}MR^2. I1=12M1R12=12×2×(0.2)2=0.04 kg m2I_1 = \frac{1}{2} M_1 R_1^2 = \frac{1}{2} \times 2 \times (0.2)^2 = 0.04\text{ kg m}^2 I2=12M2R22=12×4×(0.1)2=0.02 kg m2I_2 = \frac{1}{2} M_2 R_2^2 = \frac{1}{2} \times 4 \times (0.1)^2 = 0.02\text{ kg m}^2 Initial angular momentum of the system, Li=I1ω1+I2ω2L_i = I_1\omega_1 + I_2\omega_2 Li=(0.04×50)+(0.02×200)=2+4=6 kg m2 s−1L_i = (0.04 \times 50) + (0.02 \times 200) = 2 + 4 = 6\text{ kg m}^2\text{ s}^{-1} When the two discs are brought in contact, they will rotate together with a common final angular velocity ω\omega due to internal friction between them. There is no net external torque on the system along the axis of rotation. By conservation of angular momentum: Li=LfL_i = L_f 6=(I1+I2)ω6 = (I_1 + I_2)\omega 6=(0.04+0.02)ω6 = (0.04 + 0.02)\omega 6=0.06ω6 = 0.06\omega ω=60.06=100 rad s−1\omega = \frac{6}{0.06} = 100\text{ rad s}^{-1}

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 motionrotatingnormalpassingthroughcentres

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