Deduce The Weight Of A Truck From Its Flat Tires

Classical Mechanics Level 5

Four rubber tires of outer radius 0.5 m, inner radius 0.1 m, and width 0.2 m are inflated with air to a gauge pressure of 200 kPa. The tires are then attached to a truck and the truck is placed on the ground at sea level. The bottom of the tires very quickly squish by 5 centimeters but the tires retain their shape otherwise. What is the total mass of the truck and tires in kg?

Details:
The acceleration due to gravity is \(-9.8~m/s^2\).
The truck's weight is distributed equally on all four tires.
Assume air is completely made up of \(O_2\) and \(N_2\). (Hint: This information is necessary for this problem.)
Atmospheric pressure at sea level is 101.325 kPa.
You may neglect any 'surface tension' of the tires.

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