Question

A 1500-kg car rests on four tires, each of which is inflated to a gauge pressure of 200 kPa. If the four tires support the car's weight equally, what is the area of contact of each tire with the road?

• A. 423 $c{m}^2$
• B. 184 $c{m}^2$
• C. 842 $c{m}^2$
• D. 178 $c{m}^2$

Answer 1

The correct option is B

184 $c{m}^2$

The area of contact of each tire with the road is related to the weight on each tire and the pressure in the tire through the definition of pressure. Since, WEIGHT OF THE CAR WOULD BE BALANCED EQUALLY BY ALL THE FOUR TYRES. So, the normal reaction on all the four tyres would be equal. So, for one tyre:-
$A=\frac{\frac{1}{4}W}{P_{gauge}}=\frac{mg}{4P_{gauge}}$
Substituting numerical values and on evaluating A, we get
$A=\frac{\left(1500kg\right)\left(\frac{9.81m}{s^2}\right)}{4\left(200000Pa\right)}=184c{m}^2$