Question

An insect is crawling up a fixed hemispherical bowl of radius R. If the coefficient of friction is 1/3, then the height upto which insect can crawl is:

• A. 2 % of R
• B. 3 % of R
• C. 4 % of R
• D. 5 % of R

Answer 1

The correct option is D 5 % of R

Referring figure:
$F=\omega sina$ and $N=\omega cosa$
$mgsina=F,tana=\frac{F}{N}=\frac{1}{3}$
But, $tan(\frac{\pi }{2}-a)=cota=\frac{x}{\sqrt{R^2-x^2}}$
$x=\frac{3R}{\sqrt{10}}=0.949R$
Now, $h=R-x$
$=0.051R$

$=5$ % of $R$