Question

A vehicle is travelling with uniform speed along concave road and then along convex road of same radius of curvature. If the normal reaction on the vehicle is half of its weight as it reaches highest point of convex road, then normal reaction on the vehicle as it reaches lowest point of concave road is:

• A. twice weight of vehicle
• B. thrice weight of vehicle
• C. $1.5$ times weight of vehicle
• D. $\sqrt{2}$ times weight of vehicle

Answer 1

Answer: (C)

$1.5$ times weight of vehicle

In case of convex

$mg-N_2=\frac{m{V}^2}{R}-\left(1\right)$

In case of concave

$N_1-mg=\frac{m{V}^2}{R}-\left(2\right)$
Given $N_2=\frac{mg}{2}$
$\therefore In-\left(1\right),\frac{mg}{2}=\frac{m{V}^2}{R}$
put it in - (2)
$N_1-mg=\frac{mg}{2}$
$N_1=\frac{3}{2}mg$