Tyre of a bicycle has volume 2 10⁻³ ~m ^3 . Initially, the tube is filled 75 % of its volume by air at atmospheric pressure 10^5 Nm ⁻² . When a rider is on the bicycle, the area of contact of tyre with road is 24 10⁻⁴ ~m ^2 . The mass of rider with bicycle is 120 ~kg . If a pump delivers a volume 500 ~cm ^3 of air in each stroke, then the number of strokes required to inflate the tyre is (g=10 ~ms ⁻² )

Step-by-step solution

Pressure against which pump has to deliver air = Pressure due to weight of rider and cycle + Atmospheric pressure initially inside tyre = F A +p_ atm = 120 10 24 10⁻⁴ +1 10^5=6 10^5 N m ^2 Number of moles of air in the tube n₁= pV RT = 6 10^5 2 10⁻³ RT Volume of these moles at atmospheric pressure is aligned V₁ & = n R T p_ atm = 6 10^5 2 10⁻³ 1 10^5 & =12 10⁻³ ~m ^3 aligned Initial volume of air inside tyre V₀= 75 100 2 10⁻³=1.5 10⁻³ ~m ^3 So, to inflate the tube volume to be pumped in is aligned V₂ & =V₁-V₀=(12-1