Question

A stone of mass $1kg$ is tied of the end of a string $1m$ long. It is whirled in a vertical circle. If the velocity of stone at the top is $4m/s$. What is the tension in the string at the lowest point?

Take $g=10m/s^2$

• A. $6N$
• B. $66N$
• C. $5.2N$
• D. $76N$

Answer 1

The correct option is B $66N$

Let the velocity at lowest point is $v$ and at highest point be $u$, then according to law of conservation of energy.
energy at lowest point= energy at highest point.

$\Rightarrow \frac{1}{2}m{v}^2=mg\left(2r\right)+\frac{1}{2}m{u}^2\Rightarrow v=\sqrt{u^2+4rg}=\sqrt{4^2+(4\times 1\times 10)}=\sqrt{56}$
At lowest point,

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

$\Rightarrow T=mg+\frac{m{v}^2}{r}=mg+\frac{m(\sqrt{56}{)}^2}{r}$ $(r=1)$

$\Rightarrow T=mg+56m=66\times m=66\times 1=66N$.