Question

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

• A. $2.5$ times weight of the vehical
• B. $1.5$ times weight of the vehical
• C. Twice the weight of the vehical
• D. Thrice the weight of the vehical

Answer 1

Answer: (B)

$1.5$ times weight of the vehical

Let Normal reaction is $N_1$

Normal reaction in the case of highest point of convex road :

$N_1=mg-\frac{m{v}^2}{r}$

And

$N_1=\frac{mg}{2}$ (given )

Hence,

$\frac{mg}{2}=mg-\frac{m{v}^2}{r}$

$\frac{m{v}^2}{r}=\frac{mg}{2}$

Normal reaction on lowest point of concave road :

$N_2=mg+\frac{m{v}^2}{r}$

$=mg+\frac{mg}{2}$

$=\frac{3mg}{2}$

$=1.5$ times

Therefore $1.5$ times weight of the vehicle.

Hence, option $B$ is the correct answer.