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

The correct option is C

$F_C$ is maximum of the three forces.

Let's draw free body diagram of each car and see

$F_A$ is the normal on car by bridge

$F_A$ = mg ......... (i)

Car will push bridge with equal force downward. ( newton's 3rd law )
For car B
$mg-F_B=\frac{m{v}^2}{R}$
$\Rightarrow F_B=mg-\frac{m{v}^2}{R}$ ...........(ii)
For car C
$F_C-mg=\frac{m{v}^2}{R}$
$\Rightarrow F_C=\frac{m{v}^2}{R}+mg$
$\therefore F_C>F_A>F_B$