Question

Coefficient of friction between a tool and grinding wheel is $\mu$. Power developed in watt by the wheel of radius r running at n revolutions per second when tool is pressed to the wheel with F' kgf is

• A. $\mu F^{\prime }r\left(2\pi n\right)$
• B. $\mu F^{\prime }gr\left(2\pi n\right)$
• C. $\mu F^{\prime }r$
• D. $\mu F^{\prime }g$

Answer 1

The correct option is B $\mu F^{\prime }gr\left(2\pi n\right)$

Using $P=Fv$, we get
$P=Fr\omega$ $(\because v=r\omega )$
Here $F=\mu N$
(where N is normal reaction)
$=\mu F^{\prime }g$ $(\because 1kgf=gnewton)$
$\therefore P=\mu F^{\prime }grw=2\pi \mu n{F}^{\prime }gr$
$(\because \omega =2\pi r)$