Question

A car of mass $1000\text{kg}$ negotiates a banked curve of radius $90\text{m}$ on a frictionless road. If the banking angle is ${45}^{\circ }$, the speed of the car is:
Take $g=10{\text{m/s}}^2$

• A. $20\text{m/s}$
• B. $30\text{m/s}$
• C. $15\text{m/s}$
• D. $25\text{m/s}$

Answer 1

The correct option is B $30\text{m/s}$

Mass of car, $m=1000\text{kg}$
Radius of curve, $r=90\text{m}$
Banking angle, $\theta ={45}^{\circ }$

The relation between permissible speed and banking angle is ,
$\tan \theta =\frac{v^2}{rg}$
$\Rightarrow v=\sqrt{rg\tan \theta }$
$\Rightarrow v=\sqrt{90\times 10\times \tan {45}^{\circ }}$
$\Rightarrow v=30\text{m/s}$
Speed of the car is $30\text{m/s}$