Question

A car is moving in a circular horizontal track with a constant speed. The centripetal force acting on the car is $75\text{N}$ . If the car’s speed is doubled, what is the new centripetal force required for the car to drive on the same circular track?

• A. $150\text{N}$
• B. $37.5\text{N}$
• C. $75\text{N}$
• D. $300\text{N}$

Answer 1

The correct option is D $300\text{N}$

Let, mass of a car be $m$
Radius of circular track be $r$
Initial speed of car be $v_1$
Final speed of car be $v_2$

As car's speed is doubled, $v_2=2v_1$,


We know that the centripetal force $F_c$ is,
$F_c=\frac{m{v}^2}{r}$

For same mass and radius of curvature(as the particle is rotating in same circular path)

$\Rightarrow F\propto v^2$
$\Rightarrow \frac{F_1}{F_2}=\frac{v_1^2}{v_2^2}$
$\Rightarrow F_2=\frac{v_2^2}{v_1^2}\times F_1=4F_1=4\times 75=300\text{N}$

Hence option D is the correct answer.