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

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

Tardigrade Admin · Accepted Answer

For speed v, we have tan θ=(v2/r g)=(v2/20 g) If v'=v+10 % of v=1.1 v, then tan θ =(v' 2/r'g)=((1.1 v)2/r' g) ⇒ (1/20) =(1.21/r prime) ⇒ r'=20 × 1.21=24.2 m

Q. 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

$16 m$

$18 m$

$24.2 m$

$30.5 m$

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

Q. 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

16m

18m

24.2m

30.5m