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 N m - 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 m s - 2

Step-by-step solution

Given, Initial volume, V 0 = 75 100 × 2 × 10 - 3   m 3 = 1 . 5 × 10 - 3   m 3 and net pressure on tyre is, P = m g A + P 0 = 120 × 10 24 × 10 - 4 + 10 5 = 6 × 10 5   N   m - 2 Using the ideal gas equation, P V = n R T ⇒ n = P V R T = 6 × 10 5 × 2 × 10 - 3 R T . . . 1 again using the ideal gas equation, P 0 V 1 = n R T , from equation 1 , 10 5 × V 1 = 6 × 10 5 × 2 × 10 - 3 ⇒ V 1 = 12 × 10 - 3   m 3 So change in