Question

Suppose a car's standard tires are replaced with tires
$1.50$ times larger in diameter. What will the car's speedometer reading be?

• A. $2.25$ times too high
• B. $2.25$ times too low
• C. $1.50$ times too low
• D. $1.50$ times too high

Answer 1

The correct option is C $1.50$ times too low

The speedometer measures the number of revolutions per second of the tires. $A$ larger tire will rotate fewer times compared to smaller tire to cover the same distance. The speedometer reading is assumed to be proportional to the rotation rate of the tires. $\omega =\frac{v}{R}$ for a standard tire radius $R,$ but for tire of radius $1.5R$ the reading is
$\omega =\frac{v}{\left(1.5\right)R}$ , $i.e.,$ $1.5$ times smaller. For example: When the car travels at $15km/h,$ the speedometer reads $10km/h$
Final Answer: $\left(c\right)$