| Statement I: The safe velocity limit for taking- a turn on an unbanked road is \[v=\sqrt{\mu rg}.\] |
| Statement II: Banking of roads will increase the value of limiting velocity. |
A) Statement I is true; Statement B is true; Statement B is not a correct explanation for Statement I,
B) Statement I is true; Statement II is false.
C) Statement I is false; Statement II is true.
D) Statement I is true; Statement II is true; Statements is the correct explanation for Statement I.
Correct Answer: A
Solution :
We know that on an unbanked road the friction provides the necessary centripetal force which is \[\frac{m{{v}^{2}}}{r}=F=\mu R=\mu mg\] \[\Rightarrow \] \[v=\sqrt{\mu rg}\] This implies that with increase in friction, safe velocity increases. At banking angle of \[\theta \], its limiting velocity is given by \[v=\sqrt{\frac{rg(\mu +\tan \theta )}{(1-\mu \tan \theta )}}\] Thus, with increase of banking angle, limiting velocity increases.
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