An insect crawl up a hemispherical surface very slowly (see the figure). The coefficient of friction between…

Q: An insect crawl up a hemispherical surface very slowly (see the figure). The coefficient of friction between the surface and the insect is 1/3. If the line joining the centre of the hemispherical surface to the insect makes an angle α with the vertical, the maximum possible value of α is given
Numerical

(a) cot α =3

(b) tan α =3

(c) sec α =3

(d) cosec α =3

Ans: (a)

Sol:  N = m g cosα …(i)

f = m g sinα  …(ii)

$\large \frac{f}{N} = tan\alpha$

$\large \mu= tan\alpha$

$\large \frac{1}{3} = tan\alpha$