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 minimum at the highest position of the circular path.


At any $\theta$, the equilibrium equation for stone,

$T-\text{mg cos}\theta =\frac{m{v}^2}{R}$

$\Rightarrow \text{T = mg cos}\theta +\frac{m{v}^2}{R}$

Since, $v$ is constant,
$\Rightarrow T$ will be minimum when $\cos \theta$ is minimum.

$\Rightarrow \theta ={180}^{\circ }$ corresponds to $T_{\text{minimum.}}$

Hence, $\left(A\right)$ is the correct answer.