Question

If the coefficient of friction between an insect and bowl is $\mu$ and the radius of the bowl, is r, the maximum height to which the insect can crawl in the bowl is?

• A. $\frac{r}{\sqrt{1+{\mu }^2}}$
• B. $r[1-\frac{1}{\sqrt{1+{\mu }^2}}]$
• C. $r\sqrt{1+{\mu }^2}$
• D. $r\sqrt{1+{\mu }^2}-1$

Answer 1

The correct option is B $r[1-\frac{1}{\sqrt{1+{\mu }^2}}]$

$N=W\cos \theta$

$F=W\sin \theta$

$\frac{F}{N}=\tan \theta =h$

$\cos \theta =\frac{1}{\sqrt{{\mu }^2+1}}$

$\frac{r-h}{r}=\frac{1}{\sqrt{{\mu }^2+1}}$

$h=r(1-\frac{1}{\sqrt{{\mu }^2+1}})$