Question

A mass $m$ is revolving in a vertical circle at the end of a string of length $20\text{cms}$. By how much does the tension of the string at the lowest point exceed the tension at the topmost point

• A. $6mg$
• B. $2mg$
• C. $mg$
• D. $4mg$

Answer 1

The correct option is A $6mg$

As per the question, the situation can be represented as


We have the force equation as
$T_{Lower}=mg+\frac{m{u}^2}{r}$
$T_{Upper}=\frac{m{v}^2}{r}-mg$
So we have
$T_{Lower}-T_{Upper}=\frac{m}{r}(u^2-v^2)+2mg$...(1)
Also, we have
$u^2-v^2=\left[\right(\sqrt{5rg}{)}^2-\left(\sqrt{rg}{)}^2\right]=4rg$...(2)
Putting value of (2) in (1) we have
$T_{Lower}-T_{Upper}=\frac{m}{r}\times 4rg+2mg=6mg$