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

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

Tardigrade Admin · Accepted Answer

tan θ =(v2/r g) ⇒ r propto v2 (r2/r1)=((v2/v1))2 or (r2/20)=((1.1 v/v))2 ⇒ r2=24.2 m

Q. 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

$22 m$

$40 m$

$24.2 m$

$14.4 m$

$t an θ = \frac{v ^{2}}{r g}$
$\Rightarrow r \propto v^{2}$
$\frac{r _{2}}{r _{1}} = (\frac{v _{2}}{v _{1}})^{2}$
or $\frac{r _{2}}{20} = (\frac{1.1 v}{v})^{2}$
$\Rightarrow r_{2} = 24.2 m$

Q. 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 20m to

22m

40m

24.2m

14.4m