Question

A stone is fastened to one end of a string and is whirled in a vertical circle of radius $10\text{m}$. Find the minimum speed the stone can have at the highest point on the circle.
[Take$g=10{\text{m/s}}^2$]

• A. $10\text{m/s}$
• B. $12\text{m/s}$
• C. $5\text{m/s}$
• D. $0$

Answer 1

The correct option is A $10\text{m/s}$

At the highest point, forces acting on the stone are shown below.



So, at the highest point, net force towards the centre is given by

$F_{centre}=T+mg$

Let the minimum speed at highest point is $v$.

$\frac{m{v}^2}{R}=T+mg$

For $v$ to be minimum, $T$ should be minimum, i.e. zero

$\therefore T=0$

$\Rightarrow mg=\frac{m{v}^2}{R}$

$\Rightarrow v=\sqrt{Rg}=\sqrt{10\times 10}$

$\therefore v=10\text{m/s}$

Therefore, option $\left(A\right)$ is correct.

Why this question ? Tip: In vertical circle motion, at the highest point, required centripetal force is provided by gravitational force only.