Question

When a car is moving along a circle on a level road the centripetal force is provided by $f$, where $f$ denotes as:

• A. $f<{μ}_{s}N=\frac{m{v}^2}{r}$
• B. $f≤{μ}_{s}N=\frac{m{v}^2}{r}$
• C. $f={μ}_{s}N=\frac{m{v}^2}{r}$
• D. $f={μ}_{k}N=\frac{m{v}^2}{r}$

Answer 1

Answer: (B)

Centripetal force $f≤{μ}_{s}N=\frac{m{v}^2}{r}$ used in moving a car on a circular road. When car moves with speed $v$
centripetal acceleration required $=\frac{v^2}{r}$.

$a=\frac{v[(−\sin θ\hat{i})+(\cos θ\hat{j})]−\hat{v}}{(rθ/v)}$
$a=\frac{v^2}{r}\left(−\frac{\sin θ}{θ}\hat{i}−\frac{2{\sin }^2\frac{θ}{2}}{θ}\hat{j}\right)$
for $θ→0\text{ a }=\frac{v^2}{r}(−\hat{i})$
So, acceleration is $\frac{v^2}{r}$ towards centre at $P$ so friction of ground provides centripetal force
${μ}_s=$ coefficient of static friction