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 $100 \mathrm {~cm} ^ { 2 } ?$
A) $2.9 \times 10 ^ { 5 } \mathrm {~Pa}$
B) $12 \times 10 ^ { 5 } \mathrm {~Pa}$
C) $2.9 \times 10 ^ { 4 } \mathrm {~Pa}$
D) $12 \times 10 ^ { 4 } \mathrm {~Pa}$

Question

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  $100 \mathrm {~cm} ^ { 2 } ?$
A) $2.9 \times 10 ^ { 5 } \mathrm {~Pa}$
B) $12 \times 10 ^ { 5 } \mathrm {~Pa}$
C) $2.9 \times 10 ^ { 4 } \mathrm {~Pa}$
D) $12 \times 10 ^ { 4 } \mathrm {~Pa}$

Quizplus · Accepted Answer

The weight of the car is supported equally by four tires, so each tire supports 1/4 of the total weight. The total weight of the car is $1200 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 11760 \, \text{N}$. Therefore, each tire supports $11760 \, \text{N} / 4 = 2940 \, \text{N}$. The area of contact per tire is $100 \, \text{cm}^2 = 0.01 \, \text{m}^2$. Pressure is force divided by area, so the required gauge pressure is $2940 \, \text{N} / 0.01 \, \text{m}^2 = 2.9 \times 10^5 \, \text{Pa}$.

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