Question

The roadway bridge over a canal is in the form of an arc of a circle of radius $20m$. What is the maximum speed with which a car can cross the bridge without leaving the ground at the highest point.

• A. $10m{s}^{-1}$
• B. $12m{s}^{-1}$
• C. $14m{s}^{-1}$
• D. $16m{s}^{-1}$

Answer 1

The correct option is C $14m{s}^{-1}$

Given data,

$R=20m$

$g=9.8m/s^2$

$V_{max}=?$

For maximum velocity, weight of the car balances the cetrifugal force acting on it.

$\frac{V^2}{R}=g$

$\Rightarrow V=\sqrt{Rg}$

$\Rightarrow V=\sqrt{20\times 9.8}=\sqrt{196}$

$\Rightarrow V_{max}=14m/s$