Question

The vertical section of the road over a bridge is a circle of radius $100.2m$. A car has its center of mass $0.8m$ above the ground. The greatest speed at which the car crosses the bridge without loosing contact with the road at the highest point is: $(g=9.8{m/s}^2)$

• A. $21.4m/s$
• B. $31.5m/s$
• C. $10.0m/s$
• D. $51.5m/s$

Answer 1

The correct option is B $31.5m/s$

actual radius of circular motion $r=\sqrt{R^2+h^2}$

Let assume ${\mu }_s=1for{V}_{max}$

$\frac{m{v}^2}{r}=\mu mg$ [cancle $m$ both sides]

$v=\sqrt{\mu gr}$

$v=\sqrt{1\times 9.8\times \sqrt{R^2+h^2}}$

$v=\sqrt{9.8\times 100.99}$

$v=31.5m/s$

Hence, the option $\left(B\right)$ is the correct answer.