A) \[\theta ={{\tan }^{-1}}\,\left( \frac{{{v}^{2}}}{rg} \right)\]
B) \[\theta ={{\tan }^{-1}}\,\left( \frac{v}{rg} \right)\]
C) \[\theta ={{\tan }^{-1}}\,\left( \frac{{{r}^{2}}}{vg} \right)\]
D) \[\theta <{{\tan }^{-1}}\,\left( \frac{{{v}^{2}}}{rg} \right)\]
Correct Answer: D
Solution :
The maximum permissible speed for a vehicle so, that it does not skid \[{{v}_{\max }}=\sqrt{\mu rg}\] \[=\sqrt{rg\,\,\tan \theta }\] So, the vehicle will skid, if \[\theta <{{\tan }^{-1}}\left[ \frac{{{v}^{2}}}{rg} \right]\]
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