Question

A chain of $125$ links is $1.25m$ long and has a mass of $2\text{kg}$. With the ends fastened together, it is set rotating at $3000\text{rpm}$. The centripetal force(in $\text{N}$) on each link is( consider $\pi =3.14$)

Answer 1

Mass of each link, $m=\frac{2}{125}kg$
Radius, $r=\frac{1.25}{2\pi }m$
Angular velocity, $\omega =2\pi \times \frac{3000}{60}{\text{rad s}}^{-1}=100\pi {\text{rad s}}^{-1}$
Centripetal force
$F=mr{\omega }^2$
or $F=\frac{2}{125}\times \frac{1.25}{2\pi }\times (100\pi {)}^2$
$=\frac{1}{100\pi }\times 100\pi \times 100\pi$
$=100\pi =100\times 3.14=314\text{N}$