Question

A car has to negotiate a curve of radius $200\text{m}$. By how much should the outer side of the road be raised with respect to the inner side for a speed of $72\text{km/h}$. The width of the road is $1\text{m}$. $(g=10{\text{m/s}}^2)$

• A. $0.2\text{cm}$
• B. $2\text{cm}$
• C. $20\text{cm}$
• D. $\text{None of these}$

Answer 1

The correct option is C $20\text{cm}$

Given, $v=72\text{km/h}=72\times \frac{5}{18}=20\text{m/s}$
$w=1\text{m},r=200\text{m}$
To negotiate the curve, the condition is
$\tan \theta =\frac{v^2}{rg}$


Also, from the figure, we know
$\tan \theta =\frac{h}{w}$
$\therefore \frac{v^2}{rg}=\frac{h}{w}$
$\Rightarrow h=\frac{v^{2}w}{rg}=\frac{{20}^2\times 1}{200\times 10}=0.2\text{m}$
$\therefore h=0.2\text{m}=20\text{cm}$