An insect crawls up a hemispherical surface very slowly as shown in the figure. The coefficient of static friction between the insect and the surface is $\frac{1}{3}$ . If the line joining the centre of the hemispherical surface to the insect makes an angle $α$ with the vertical, then the maximum possible value of $α$ is given by

Question

An insect crawls up a hemispherical surface very slowly as shown in the figure. The coefficient of static friction between the insect and the surface is

\frac{1}{3}

. If the line joining the centre of the hemispherical surface to the insect makes an angle

α

with the vertical, then the maximum possible value of

α

is given by

Toppr Admin · Accepted Answer

Mgsin-x3B1-x3BC-mgcos-x3B1-x2234-tan-x3B1-x3BC-or cot-x3B1-1-x3BC-3

mgsinα=μmgcosα∴tanα=μor cotα=1μ=3

$m g s i n α = μ m g c o s α ∴ t a n α = μ$
or $c o t α =$ $\frac{1}{μ}$ $= 3$