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 car is (Take $g=10{\text{m/s}}^2$)

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

Answer 1

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


By the free body diagram and writing the force equation we get,
$N\cos \theta =mg...\left(i\right)$
$N\sin \theta =\frac{m{v}^2}{r}...\left(ii\right)$
Now by dividing both the above equations, we get,
$\theta ={\tan }^{-1}\left(\frac{v^2}{rg}\right)$
where, $v$ = speed and r = radius
For banking, $\tan \theta =\frac{v^2}{rg}$
$\Rightarrow \tan {45}^{\circ }=\frac{v^2}{90\times 10}=1$
$\Rightarrow v^2=900$
$\Rightarrow v=\sqrt{900}\text{m/s}=30\text{m/s}$