Question

The road way bridge over a canal is in the form of an arc of a circle of radius $20m$. What is the minimum speed with which a car can cross the bridge without leaving contact with the ground at the highest point $(g = 9.8\mspace{6mu} m/s^{2})$

• A. $7\mspace{6mu} m/s$
• B. $14\mspace{6mu} m/s$
• C. $289\mspace{6mu} m/s$
• D. $5\mspace{6mu} m/s$

Answer 1

Answer: (B)

$14\mspace{6mu} m/s$

Answer 2

At the highest point of the bridge for critical condition $mg - \frac{mv^{2}}{r} = 0$ ⇒ $\frac{mv^{2}}{r} = mg$

∴ ${v\sqrt{gr}}_{\max} = \sqrt{9.8 \times 20} = \sqrt{196} = 14m/s$