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Tyre of a bicycle has volume $2000 c m^{3} .$ Initially the tube is filled to $0.75$ of its volume by air at atmospheric pressure of $ρ_{0} = 10^{5} N / m^{2}$ . Area of contact of both tyres with the road is $A = 24 c m^{2}$ when total mass of bicycle and its rider is $m = 120 k g .$ Number of strokes of pump, which delivers $V = 500 c m^{3}$ volume of air in each stroke, required to inflate the tyre is $7 x .$ Find the value of x. Assume that are of contact of tyre with road remains unchanged.

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answer is 3.

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Detailed Solution

N on each tyre = 600 N
Excess pressure inside tyre $= \frac{N}{A} = \frac{600}{12} \times 10^{4}$

$Δ P = 5 \times 10^{5}$

$P_{n e t} i n t y r e = 6 \times 10^{5} P a b u t \frac{3 p_{0} v_{0}}{4} + x \frac{p_{0} v_{0}}{4} = 6 p_{0} v_{0} \frac{3}{4} + \frac{x}{4} = 6 x = 21 s t r o k e s$

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