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 $F_{A}, F_{B}$ 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

Answer: (C)

(i) For Plane Bridge
$F_{A}=N=Mg$
(ii) For Convex Upward Bridge
$F_{B}=N=Mg-\frac{Mv^{2}}{r}$
(iii) For Concave Downward Bridge
$N-Mg=\frac{Mv^{2}}{r}$
$F_{C}=\frac{Mv^{2}}{r}+Mg$
$\therefore F_{C}>\,F_{A}>\,F_{B}$