question_answer

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 verticle, the maximum value of a is given by:

A)  \[\cot \alpha =3\]                   

B)  \[\sec \alpha =3\]

C)  \[cosec\alpha =3\]       

D)  None of these

Correct Answer: A

Solution :

            From FED, Friction \[f=mg\,\sin \alpha \] and        \[N=mg\,\,\cos \alpha \]                 \[\frac{F}{N}=\tan \alpha \] For maximum possible value of a friction becomes limiting friction \[\Rightarrow \]               \[\mu =\tan \alpha \] \[\Rightarrow \]               \[\cot \,\alpha =3\]