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)12 × 10⁵ Pa B)12 × 10⁴ Pa C)2.9 × 10⁵ Pa D)2.9 × 10⁴ Pa

Question

Quizplus · Accepted Answer

The total weight of the car is supported equally 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 100 cm^2.

We can use the formula:

P = F / A

Where P is the gauge pressure, F is the force on the tire, and A is the area of contact.

Substituting the given values, we get:

P = (300 kg × 9.8 m/s^2) / (100 cm^2 × 10^-4 m^2)

P = 2.94 × 10^5 Pa

Converting to gauge pressure (subtracting atmospheric pressure of 1 atm), we get:

P = 2.94 × 10^5 - 1 atm = 2.9 × 10^5 Pa = 2.9 × 10^1 kPa

Rounding to two significant figures, the answer is:

Choice C) 2.9 × 10^1 kPa (or 2.9 × 10^4 Pa)

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