Tyre of a bicycle has voulme `2xx10^(-3)m^(3)` Initially the tube is filled to `75%` of its volume by air at atmospheric pressure of `P_(0)=10^(5)N//m^(2)`. When a rider rides the bicycle the area of contact of tyre with road is `A=24xx10^(-5)m^(2)`. The mass of rider with bicycle is 120kg. The number of stokes which delivers, `V=500cm^(3)` volume of air in each stroke required to infalte the tyres is [Take `g=m//s^(2)`]

Options

A. 10
B. 11
C. 20
D. 21

Answer

D

Explanation

The pressure of air in the tube is
`P=(mg)/(A)+P_(0)`
`P=6xx10^(5)N//m^(2)`
Final volume of air in the tube is,
`V=2xx10^(-3)m^(3)`
The number of moles of air in the tube after pumping is, Initially volume of air in the tube is,
`n=(pV)/(RT)` where T is temperature
Thes n moles of air has volume `V_(1)` at atmosphere pressure given by
`V_(1)=(nRT)/(P_(0))=(6xx10^(5)xx2xx10^(-3))/(10^(5))m^(3)`
`=2xx10^(-3)m^(3)`
Initially volume of air in the tube is
`V_(0)=0.75xx2xx10^(-3)=1.5xx10^(-3)m^(3)`
So, volume of air to be pumped is,
`V=V_(1)-V_(0)=10.5xx10^(-5)m^(3)`
So, number of strokes of pump required is,
`n_(0)=(DeltaV)/(V)=(10.5xx10^(-3))/(0.5xx10^(-3))=21`