Home Physics Motion in a Plane Radius of Curvature A uniform metallic chain in a form of circul…
Physics Motion in a Plane Radius of Curvature Subjective Type
Published on: September 12, 2026

A uniform metallic chain in a form of circular loop of mass m = 3 kg with a length = 1 m rotates at the rate of n = 5 revolutions per second. Find the tension T (in Newton) in the chain.

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Text Solution

Verified by Experts
The correct answer is:
C
Given Data:
Mass of the chain, m = 3 kg
Length of the chain, \( \ell = 1 \text{ m} \)
Number of revolutions per second, n = 5

Step 1: Find radius of the circular loop
The length of the chain is equal to the circumference of the circle, so:
\[ \ell = 2\pi r \implies r = \frac{\ell}{2\pi} = \frac{1}{2\pi} \approx 0.159 \text{ m} \]

Step 2: Find angular velocity
The angular velocity (\( \omega \)) in radians per second is given by:
\[ \omega = 2\pi n = 2\pi \times 5 = 10\pi \text{ rad/s} \]

Step 3: Calculate centripetal force acting on the chain
The centripetal force (F) required to keep the chain in circular motion is:
\[ F = m \cdot a_c = m \cdot r \cdot \omega^2 \]
where \( a_c = r \cdot \omega^2 \)

So:
\[ a_c = r \cdot \omega^2 = \left(\frac{1}{2\pi}\right) (10\pi)^2 = \frac{100\pi^2}{4\pi^2} = 25 \text{ m/s}^2 \]
Then,
\[ F = m \cdot a_c = 3 \cdot 25 = 75 \text{ N} \]

Step 4: Find the tension in the chain
In a uniform circular motion, tension (T) acts towards the center, contributing to centripetal force:
\[ T = F = 75 \text{ N} \]

Thus, the tension in the chain is 75 N. Therefore, option C is correct.

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