Question

The angular speed (in rev/ min) needed for a centriguge to produce an acceleration of $1000g$ at a radius of $10cm$ is (Take $g=10m/s^2)$?

• A. $1500$ rev/min
• B. $4000$ rev/min
• C. $2000$ rev/min
• D. $3000$ rev/min

Answer 1

The correct option is D $3000$ rev/min

Given that

$r=10cm=0.1m$

$a=1000\times 10m/s^2$

$={10}^{4}m/s^2$

So ${\omega }^2=\frac{a}{r}$

$\omega =\sqrt{\frac{a}{r}}$

$=\sqrt{\frac{{10}^4}{{10}^{-1}}}$

$=316rad/s$

or $\omega =316rad/s$

So, $r=\frac{316}{2\pi }=50.3rps$

$=50r.p.s.$

or $r=3000r.p.m.$