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 force exerted by the cars on the bridges when they are at the middle of bridges then :

• 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

$F_A$, $F_B$ and $F_C$ are the magnitude
of the normal contact forces with which car and bridge exert forces on
each other.
for car 'A'
$F_A=mg$ ......... $\left(I\right)$
for car 'B'
$\frac{m{v}^2}{r}=mg-F_B$
$\Rightarrow F_B=mg-\frac{m{v}^2}{r}$ ......... $\left(II\right)$
for car 'C'
$\frac{m{v}^2}{r}=F_c-mg$
$\Rightarrow F_c=mg+\frac{m{v}^2}{r}$ ......... $\left(III\right)$
from equations $\left(III\right)$, $\left(II\right)$ and $\left(I\right)$, we see that
$F_c>F_A>F_b$