Question

A truck is travelling at uniform speed along concave road, convex road of same radius of curvature and then along straight horizontal road. If the normal reactions $5\times {10}^{5}N,$ ${10}^{5}N$ act on the truck at the lowest, highest points of concave, convex roads respectively, the normal reaction on the truck when it travelling on horizontal road is:

• A. $2\times {10}^{5}N$
• B. $3\times {10}^{5}N$
• C. $4\times {10}^{5}N$
• D. $6\times {10}^{5}N$

Answer 1

The correct option is B $3\times {10}^{5}N$

Speed is $V$
At concave curvature
$N_1-mg=\frac{m{V}^2}{R}-\left(1\right)$
At convex curvature
$mg-N_2=\frac{m{V}^2}{R}-\left(2\right)$
Subtracting (1) - (2)
$N_1+N_2=2mg$
$\frac{6\times {10}^5}{2}=mg$
$mg=3\times {10}^{5}N$
At horizontal road
$mg=N_3$
$N_3=3\times {10}^{5}N$