JEE Main & Advanced Physics NLM, Friction, Circular Motion Sample Paper Topic Test - Friction

  • question_answer
    An insect crawls up on a hemispherical surface very slowly (figure). The coefficient of friction between the insect and the surface is \[1/3\]. If the line joining the centre of hemispherical surface of the insect makes an angle a with the vertical, the maximum possible value of a is given by                         

    A) cot\[\alpha \] = 3    

    B) tan\[\alpha \]= 3

    C) sec\[\alpha \]= 3           

    D) cosec\[\alpha \]= 3

    Correct Answer: A

    Solution :

    Idea Angle will be maximum, when insect will crawl upto a certain height at which maximum static friction on insect will be counter balanced by its tangential component of its weight.
    To avoid slipping, \[{{f}_{r}}=mg\,\sin \,\,\alpha \] at maximum\[\alpha \]
    \[\mu N=mg\sin \alpha \]
    \[\Rightarrow \]\[\mu \,mg\cos \alpha =mg\sin \alpha \]
    \[\therefore \,\,\mu \,\,=\,\,\tan \,\alpha \]
    \[\Rightarrow \]\[\tan \alpha =\frac{1}{3}\] \[\left( \text{as,}\mu \,\text{=}\frac{1}{3} \right)\]
                \[\therefore \]\[\cot \alpha =3\]

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