A cylinder of water volume V is emptied through a much smaller orifice of area s by a constant piston force during time t. Neglect viscosity/friction. If work is ρV³/(a sᵇ t²), where a and b are integers, calculate a + b. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A cylinder of water volume V is emptied through a much smaller orifice of area s by a constant piston force during time t. Neglect viscosity/friction. If work is ρV³/(a sᵇ t²), where a and b are integers, calculate a + b. [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Liquid volume V must leave through orifice area s in duration t, so outflow speed is v = V/(st). Step 2 — Bernoulli equation for negligible piston speed and negligible friction gives required gauge pressure ΔP = (1/2)ρv². Step 3 — Piston work is W = ΔP × displaced volume V = (1/2)ρ (V/(st))² V. Step 4 — W = ρV³/(2s²t²). Thus a = 2, b = 2, a + b = 4.