Question

A plastic circular disc of radius R is placed on a thin oil film spread over a flat horizontal surface the torque required to spin the disc about its central vertical axis with a constant angular velocity is proportional to
A. `R^(2)`
B. `R^(2)`
C. `R^(4)`
D. `R^(6)`

Answer 1

Correct Answer - C
Let coefficient of viscosity & thickness of film rightarrow eta & x respectively viscous force on element ring is
`dF=eta(2pirdr)[(wr-0)/x]`
`d(tau)=(df)r`
`:.tau=(eta2piw)/t underset(0)overset(R)intr_(3) dr=((n(2pi)w)/(4x))R^(4)`
`:. tauproptoR^(4)`