An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is 1/3. If the line joining the centre of the hemispherical surface to the insect makes an angle a with the vertical, the maximum possible value of a so that the insect does not slip is given by

Question

An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is 1/3. If the line joining the centre of the hemispherical surface to the insect makes an angle a with the vertical, the maximum possible value of a so that the insect does not slip is given by (A) cot α = 3 (B) sec α = 3 (C) cosec α= 3 (D) cos α = 3

Tardigrade Admin · Accepted Answer

The insect crawls up the bowl upto a certain height h only till the component of its weight along the bowl is balanced by limiting frictional force.
For limiting condition at point A

R = m g cos α ... (i)

F_{1} = m g s in α ... (ii)

Dividing eq.

(ii)

by

(i)

t an α = \frac{1}{co t α} = \frac{F _{1}}{R} = μ [A s F_{1} = μ R]

\Rightarrow t an α = μ = \frac{1}{3} [∵ μ (

Given

])

∴ co t α = 3

$co t α = 3$

$sec α = 3$

$cosec α = 3$

$cos α = 3$

cotα=3

secα=3

cosecα=3

cosα=3

$co t α = 3$

$sec α = 3$

$cosec α = 3$

$cos α = 3$