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

Answer: (B)

minimum at the highest position of the circular path.

Answer 2

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 $T_{minimum}$.