This NEET Physics problem tests your understanding of rotational motion, torque, angular acceleration, and the relationship between force and angular velocity. Here is a clear, step-by-step explanation with formulas written in MathJax-friendly format.
Q. A string is wrapped around the rim of a wheel of moment of inertia \( I = 0.40\, \text{kg m}^2 \) and radius \( r = 10\,\text{cm} = 0.10\,\text{m} \). The wheel is free to rotate about its axis and is initially at rest. The string is pulled with a constant force of \( F = 40\,\text{N} \). What is its angular velocity after \( t = 10\,\text{s} \)?
(NEET 2017)
1. 40 rad/s
2. 50 rad/s
3. 100 rad/s
4. 25 rad/s
Step-by-Step Solution
Torque produced by the force:
\[ \tau = F \times r = 40 \times 0.10 = 4\ \text{N·m} \]
Angular acceleration:
\[ \alpha = \frac{\tau}{I} = \frac{4}{0.40} = 10\ \text{rad/s}^2 \]
Using the rotational kinematic equation:
\[ \omega = \omega_0 + \alpha t \]
Since the wheel starts from rest: \[ \omega = 0 + 10 \times 10 = 100\ \text{rad/s} \]✔ Correct Option: 3. 100 rad/s
Why this concept matters in NEET?
Rotational motion questions like torque, moment of inertia, and angular acceleration regularly appear in NEET because they blend Newtonian mechanics with practical physical systems. A simple setup like a wheel and string is enough to test understanding of real-world rotational dynamics.
Keep practicing such questions to master the core mechanics behind rolling and rotational systems.
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