question_answer

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/sec. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with track is [IIT 1992]

A)             Zero    

B)             \[{{30}^{o}}\]

C)             \[{{45}^{o}}\]         

D)             \[{{60}^{o}}\]

Correct Answer: C

Solution :

    \[\tan \theta =\frac{{{v}^{2}}/r}{g}=\frac{{{v}^{2}}}{rg}\]             \ \[\theta ={{\tan }^{-1}}\left( \frac{{{v}^{2}}}{rg} \right)\]\[={{\tan }^{-1}}\left( \frac{10\times 10}{10\times 10} \right)\]             \ \[\theta ={{\tan }^{-1}}(1)=45{}^\circ \]