Question

Keeping the angle of banking of the road constant, the maximum speed of the vehicles is to be increased by $10\%$ . The radius of curvature of the road will have to be changed from $20 \, m$ to

• A. $22 \, m$
• B. $40 \, m$
• C. $24.2 \, m$
• D. $14.4 \, m$

Answer 1

Answer: (C)

$tan \theta =\frac{v^{2}}{r g}$
$\Rightarrow \, \, r \propto v^{2} \, \, $
$\frac{r_{2}}{r_{1}}=\left(\frac{v_{2}}{v_{1}}\right)^{2}$
or $\frac{r_{2}}{20}=\left(\frac{1.1 v}{v}\right)^{2}$
$\Rightarrow \, \, \, r_{2}=24.2 \, m$