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 α with the vertical, the max possible value of α is given by

• A. Cotα = 3
• B. Secα = 3
• C. Cosecα = 3
• D. None of these

Answer 1

Answer: (A)

Cotα = 3

Answer 2

From F.B.D.

Friction f = mg sinα

N = mg cosα

$\frac { \mathrm { f } } { \mathrm { N } }$ = tanα for maximum possible value of α.

Friction becomes limiting friction.

⇒ μ = tanα ⇒ cotα = 3 , Hence the correct choice is