Question

A stone of mass m tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is

• A. the same throughout the motion.
• B. minimum at the highest position of the circular path.
• C. minimum at the lowest position of the circular path.
• D. minimum when the rope is in the horizontal position.

Answer 1

The Correct Option is B

At any \(θ\):
\(T - mg \;\cos θ = \frac{mv^2}{R}\)

⇒ \(T = mg\; \cos θ + \frac{mv^2}{R}\)

Since \(v\) is constant,

⇒ \(T\) will be minimum when \(\cos \theta\) is minimum.

⇒ \(θ = 180°\) corresponds to \(T_{minimum}\)_.