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 $20m$ to-

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

Answer 1

Answer: (C)

$24.2m$

For speed v, we have
$\tan \theta =\frac{v^2}{rg}=\frac{v^2}{20g}$......(i)
If $v^{\prime }=v+0.1v=1.1v$, then
$\tan \theta =\frac{v^{\prime 2}}{r^{\prime }g}=\frac{{\left(1.1v\right)}^2}{r^{\prime }g}$....(ii)
Equating (1) and (ii), we get $\frac{1}{20}=\frac{1.21}{r^{\prime }}$
$\Rightarrow r^{\prime }=20\times 1.21=24.2m$