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

Q: 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 $\alpha $ with the vertical, the maximum possible value of $\alpha $ so that the insect does not slip is given by

a $\begin{array}{l} The\,{\rm{insect}}\,crawls\,up\,the\,bowl\,upto\,a\\ certain\,height\,h\,only\,till\,the\,component\\ of\,its\,weight\,along\,the\,bowl\,is\,balanced\,\\ by\,{\rm{limiting}}\,frictional\,force\\ For\,li\,miting\,condition\,at\,{\rm{point}}\,A\\ R = mg\,\cos \alpha \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)\\ {F_1} = mg\,\sin \alpha \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} \right) \end{array}$ $\begin{array}{l} Dividing\,eq.\,\left( {ii} \right)\,by\,\left( i \right)\\ \tan \,\alpha \, = \frac{1}{{\cot \,\alpha }} = \frac{{{F_1}}}{R} = \mu \left[ {As\,{F_1} = \mu R} \right]\\ \Rightarrow \,\tan \alpha \, = \mu = \frac{1}{3}\left[ {\mu = \frac{1}{3}\left( {given} \right)} \right]\\ \therefore \,\,\cot \alpha \, = 3 \end{array}$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

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 $\alpha $ with the vertical, the maximum possible value of $\alpha $ so that the insect does not slip is given by

A$\cot \,\alpha = 3$
B$\sec \,\alpha = 3$
C$\cos ec \,\alpha = 3$
D$\cos \,\alpha = 3$

AIEEE 2012,IIT 2001, Diffcult

STD 11 Science
NEET
STD 11 - 4.2. friction
Physics

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