The weight of a 1200-kg car is supported equally by the four tires, which are inflated to the same gauge pressure. What gauge pressure is required so the area of contact of each tire with the road is 100 cm²? A) 11.6 × 10⁵ Pa B) 11.6 × 10⁴ Pa C) 2.9 × 10⁵ Pa D) 2.9 × 10⁴ Pa

Question

Quizplus · Accepted Answer

The weight of the car is supported by the four tires, so the weight supported by each tire is:

W = (1200 kg)/(4) = 300 kg

The area of contact of each tire with the road is given as:

A = 100 cm^2 = 0.01 m^2

Assuming that the gauge pressure is the same in all tires, we can use the formula:

P = F/A

where F is the force exerted by each tire on the ground, given by:

F = W = 300 kg × 9.8 m/s^2 = 2940 N

Substituting the values, we get

P = 2940 N / 0.01 m^2 = 2.94 × 10^5 Pa

This is the gauge pressure required in each tire. However, the question asks for the answer in scientific notation with two significant figures. Rounding off to two significant figures and expressing in scientific notation, we get:

P = 2.9 × 10^5 Pa

which is closest to option C.

The Weight of a 1200-Kg Car Is Supported Equally by the Four