Question

The coefficient of friction between an insect and bowl is $\mu$ and the radius of the bowl ${}^{\prime }{r}^{\prime }$. The maximum height to which the insect can crawl in the bowl is:

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

Answer 1

The correct option is A $r(1-\frac{1}{\sqrt{{\mu }^2+1}})$

At maximum height insect will be in equilibrium

From FBD

$N=mgcos\theta$ and $mgsin\theta =\mu N$

$tan\theta =\mu$

From triangle

$cos\theta =\frac{h}{r}$

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

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

The maximum height to which it can crawl

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