Question

A bridge is in the form of a semi-circle of radius $10\text{m}$. The greatest speed with which a motorcycle can cross the bridge without leaving the ground at the highest point is $(g=10{\text{m/s}}^2)$ (frictional force is negligibly small)

• A. $10\sqrt{2}\text{m/s}$
• B. $100\text{m/s}$
• C. $10\text{m/s}$
• D. $10\sqrt{10}\text{m/s}$

Answer 1

The correct option is C $10\text{m/s}$

By the FBD of the motor cycle at the top we get,

Here $F_c$ is centrifugal force on motor cycle
Writing the force equation at the highest point we get,

$N+F_c=mg$
$\Rightarrow N+\frac{m{v}^2}{R}=mg$
To achieve greatest speed, without leaving the ground at highest point,
$N=0$
$\Rightarrow \frac{m{v}^2}{R}=mg$
$v=\sqrt{Rg}=\sqrt{10\times 10}$
$=10\text{m/s}$

Hence option C is the correct answer