Question

Three identical cars $A,B$ and $C$ are moving at the same speed on three bridges. The car $A$ goes on a plane bridge, $B$ on a bridge convex upward and $C$ goes on a bridge concave upward. Let $F_A,F_B$ text and $F_C$be the normal forces exerted by the cars on the bridges when they are at the middle of bridges.

• A. $F_A$ is maximum of the three forces
• B. $F_B$ is maximum of the three forces
• C. $F_C$ is maximum of the three forces
• D. $F_A=F_B=F_C$

Answer 1

The correct option is C $F_C$ is maximum of the three forces

Normal reaction for plane bridge, $F_A=mg\dots \left(i\right)$
For convex upward bridge,
$F_B=Mg-\frac{M{v}^2}{r}\dots \left(ii\right)$
For concave downward bridge,
$F_C-Mg=\frac{M{v}^2}{r}$
$F_C=\frac{M{v}^2}{r}+Mg\dots \left(iii\right)$
From equation $\left(i\right)$, $\left(ii\right)$ and $\left(iii\right)$ $F_C>F_A>F_B$