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 force on each tire is given by:

F = Weight of car/4 = (1.20 × 10^3 kg) x g/4

Where g is the acceleration due to gravity.

The area of contact of each tire is given as:

A = 1.00 × 10^-2 m x 1.00 × 10^-2 m = 1.00 × 10^-4 m^2

The pressure in each tire is given as:

P = F/A

Substituting the expressions for F and A, we have:

P = (1.20 × 10^3 kg) x g/4 x 1.01 × 10^5 Pa / (1.00 × 10^-4 m^2)

Simplifying, we get:

P = 2.94 × 10^5 Pa

or

P = 2.94 × 10^2 kPa

Thus, the required gauge pressure in each tire is 2.94 × 10^5 Pa, which is closest to option C (2.94 x 10^15 Pa).

The Weight of a Car of Mass 1