Question

A small object of mass $m$, on the end of a light cord, is held horizontally at a distance $r$ from a fixed support as shown. The object is then released. What is the tension in the cord when the object is at the lowest point of its swing?

• A. $mg/2$
• B. $mg$
• C. $2mg$
• D. $3mg$

Answer 1

The correct option is D $3mg$

When it is at point A work done by gravity $=mgR$

Applying work-energy theorem

$\Delta KE=mgR$

$\Rightarrow$ $\frac{1}{2}m{v}^2-m\frac{{\left(0\right)}^2}{2}=mgR$ (initial vel. of the particle is $0$)

$m{v}^2=2mgR$

As the particle is moving in a circle, centripetal force $\left(\frac{m{v}^2}{r}\right)$ is

acting on it upwards (towards $0$)

So,

$T-Mg=\frac{m{v}^2}{r}$

$T=\frac{m{v}^2}{r}+Mg$

As $m{v}^2=2mgR$

$T=\frac{2mgR}{R}+Mg=3Mg$