Question

A car of mass $1000\text{kg}$ negotiates a banked curve of radius $90\text{m}$ on a fictionless road. If the banking angle is ${45}^{\circ }$, the speed of the car is

• A. $30{\text{ms}}^{-1}$
• B. $20{\text{ms}}^{-1}$
• C. $10{\text{ms}}^{-1}$
• D. $5{\text{ms}}^{-1}$

Answer 1

The correct option is A $30{\text{ms}}^{-1}$


From the FBD of the car,
$N\cos \theta =mg$ ........$\left(1\right)$

Centripetal force is provided by the horizontal component of the normal force acting on the car,
$N\sin \theta =\frac{m{v}^2}{R}$ ........$\left(2\right)$

Dividing equation$\left(2\right)$ by $\left(1\right)$,
$\tan \theta =\frac{v^2}{Rg}$

$\Rightarrow v=\sqrt{Rg\tan \theta }$

$\Rightarrow v=\sqrt{90\times 10\times \tan {45}^o}=30{\text{ms}}^{-1}$

Hence, option $\left(D\right)$ is correct.