JEE ADVANCED PHYSICS QUESTION SEPTEMBER 2020
Answers
A train with cross-sectional area St is moving with speed vt inside a long tunnel of cross-sectional area S0 (S0 = 4St). Assume that almost all the air (density ρ) in front of the train flows back between its sides and the walls of the tunnel. Also, the air flow with respect to the train is steady and laminar.
Take the ambient pressure and that inside the train to be p0. If the pressure in the region between the
sides of the train and the tunnel walls is p, then P₀ - P = 7/2N ρvt². The value of N is ......
solution : From Bernoulli's equation,
P₀ + 1/2 ρvt² = P + 1/2ρv², where P is the pressure and v is the speed of air in in the region between the sides of the train and tunnel walls.
⇒(P₀ - P) = 1/2 ρ(v² - vt²) ....(1)
now from equation of continuity, A₁v₁ = A₂v₂
⇒(4St) × vt = (St + St + St) × v
⇒v = 4/3 vt .......(2)
from equations (1) and (2) we get,
P₀ - P = 1/2 ρ(16/9vt² - vt²) = 7/2(9) ρvt²
on comparing we get, N = 9
Therefore the value of N is 9
