Question

A stone of mass $1\text{kg}$ is tied with a string, and it is whirled in a vertical circle of radius $1\text{m}$. If tension at the highest point is $14\text{N}$, then velocity at the lowest point will be
$($Take value of $g=10{\text{m/s}}^2)$

• A. $3\text{m/s}$
• B. $4\text{m/s}$
• C. $6\text{m/s}$
• D. $8\text{m/s}$

Answer 1

The correct option is D $8\text{m/s}$

Let $v$ be the velocity at the highest point and $u$ at the lowest point of the vertical circular path.


At the highest point, equation of dynamics,
$T+mg=\frac{m{v}^2}{R}$
$\Rightarrow 14+10=\frac{v^2}{1}$
$\Rightarrow v^2=24$
Applying mechanical energy conservation between lowest and highest point, taking potential energy zero at lowest point.$\frac{1}{2}m{u}^2+0=\frac{1}{2}m{v}^2+mg\left(2R\right)$
$\Rightarrow \frac{1}{2}\times 1\times u^2=\frac{1}{2}\times 1\times 24+1\times 10\times 2\times 1$
$\Rightarrow u^2=64$
$\Rightarrow u=\sqrt{64}=8\text{m/s}$

Why this question? It intends to test the application of Newton's second law, concept of circular dynamics and energy conservation in a single package.