Question

An object of mass $1\text{kg}$ attached to the string of length $1\text{m}$ is whirled in a vertical circle at a constant angular speed. If the maximum tension in the string is $60\text{N}$, then what is the speed of the object at the lowest point?

• A. $\sqrt{30}\text{m/s}$
• B. $\sqrt{40}\text{m/s}$
• C. $\sqrt{50}\text{m/s}$
• D. $\sqrt{60}\text{m/s}$

Answer 1

The correct option is C $\sqrt{50}\text{m/s}$

Given:
Mass of object, $m=1\text{kg}$
Radius of circle, $R=1\text{m}$
Maximum Tension in the string, $T=60\text{N}$
We know that Tension at lowest point is maximum and given by,
$T=\frac{m{v}^2}{R}+mg$
$\Rightarrow 60=\frac{1\times v^2}{1}+1\times 10$
On solving this, we get,
$\Rightarrow v=\sqrt{50}\text{m/s}$
Hence, option $\left(c\right)$ is correct.