The weight of a car of mass 1.20 × 10³ kg is supported equally by the four tires, which are inflated to the same gauge pressure. What gauge pressure in the tires is required so the area of contact of each tire with the road is 1.00 × 10² cm²? (1 atm = 1.01 × 10⁵ Pa.) A) 11.6 × 10⁵ Pa B) 11.6 × 10⁴ Pa C) 2.94 × 10⁵ Pa D) 2.94 × 10⁴ Pa E) 2.94 × 10³ Pa

Question

Quizplus · Accepted Answer

The weight of the car, W = 1.20 × 10^4 × 9.8 N.
The area of contact of each tire with the road, A = 1.00 × 10^-2 m^2.
Let the gauge pressure in each tire be P.
According to the first equation of static equilibrium, the sum of the vertical forces acting on the car must be zero:
4P × A - W = 0
Solving for P, we get:
P = W/(4A) = (1.20 × 10^4 × 9.8)/(4 × 1.00 × 10^-2) Pa
P = 2.94 × 10^5 Pa
Converting to atm, we get:
P = 2.90 atm
Since 1 atm = 1.01 × 10^5 Pa, we have:
P = 2.90 × 1.01 × 10^5 Pa = 2.94 × 10^5 Pa
Therefore, the correct answer is choice C.

The Weight of a Car of Mass 1