A small spherical ball falling under gravity in a viscous medium heats the medium due to viscous drag force. The rate of heating is proportional to rⁿ (r = radius of the sphere). Find n.
Physics · Mixed Chapter
JEE Mains

Question

A small spherical ball falling under gravity in a viscous medium heats the medium due to viscous drag force. The rate of heating is proportional to rⁿ (r = radius of the sphere). Find n.

G1 Physics · Accepted Answer

Step 1: For steady terminal falling in the Stokes regime, vₜ∝r². Step 2: Viscous force F_d=6πηrvₜ∝r³. Step 3: Rate of viscous heating is P=F_d vₜ∝r³×r²=r⁵. Step 4: n=5.