Question

Keeping the banking angle same, to increase the maximum speed with which a vehicle can travel on the curved road by $10\%$ , the radius of curvature of the road has to be changed from $20\,m$ to

• A. $16\,m$
• B. $18\,m$
• C. $24.2\,m$
• D. $30.5\,m$

Answer 1

Answer: (C)

$24.2\,m$

Answer 2

For speed $v$, we have
$\tan \theta=\frac{v^{2}}{r g}=\frac{v^{2}}{20 g}$
If $v'=v+10 \%$ of $v=1.1 v$, then
$\tan \theta =\frac{v' 2}{r'g}=\frac{(1.1 v)^{2}}{r' g}$
$\Rightarrow \frac{1}{20} =\frac{1.21}{r^{\prime}}$
$\Rightarrow r'=20 \times 1.21=24.2\, m$