Two rotating clutch plates separated by viscous fluid transmit torque. Input and output angular velocities are ωᵢ and ωₒ. If ωₒ = ωᵢ/2, efficiency η = 1/x. Find x. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

Two rotating clutch plates separated by viscous fluid transmit torque. Input and output angular velocities are ωᵢ and ωₒ. If ωₒ = ωᵢ/2, efficiency η = 1/x. Find x. [See Image.]

G1 Physics · Accepted Answer

Step 1 — Viscous shear transmits equal torque magnitude τ from input plate to output plate under steady motion. Step 2 — Input power Pᵢ = τωᵢ; output Pₒ = τωₒ. Step 3 — Efficiency η = Pₒ/Pᵢ = ωₒ/ωᵢ. Step 4 — With ωₒ = ωᵢ/2, η = 1/2 = 1/x; x = 2.