If a hole is punctured in a tire, the gas inside will gradually leak out of it. Let's assume the following : the area of the hole is A, the tire volume is V, and the time it takes for most of the air to leak out of the tire be t. This time can be expressed in terms of the ratio `A//V`, the temperature T. the Universal gas constant R, and the mass of the gas molecules inside the tire, m. Under these assumptions, we can use dimensional analysis to find an estimate for t. Assuming this estimate to be correct, if the mass of air within a tyre is increased by `70%`, the absolute tyre temperature increased by `20%`, while the area of the punctured hole is doubled (but still small) then the time in which a tyre will go flat will

Options

A. increased by `10%`
B. increase by `25%`
C. decrease by `25%`
D. decrease by `40%`

Answer

D

Explanation

Using dimensional analysis or otherwise `t = (V)/(A) sqrt(m)/(RT) xx` some numerical factor
Substituting the values we get `(t')/(t) = (1)/(2) sqrt(1.7)/(1.2) ~~ 0.6`