Question

Assertion :A car moving on a horizontal rough road with velocity $v$ can be stopped in a minimum distance $d$. If the same car, moving with same speed $v$ takes a circular turn, then minimum safe radius can be $2d$. Reason: $d=\frac{v^2}{2\mu g}$ and minimum safe radius $=\frac{v^2}{\mu g}$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion is incorrect and Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Case 1: $d=vt-\frac{a{t}^2}{2}andv=at$

From these two equations, we get: $d=\frac{v^2}{2\mu g}$

Case 2: Centripetal Force, $m\mu g=\frac{m{v}^2}{r}$

Hence, $r=\frac{v^2}{\mu g}$

If $r$ is less than this, as $\mu$ is limited, the car would not be able to balance.

Hence, $r_{min}=2d$