Question

A plastic circular disc of radius r is placed on a thin 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 directly proportional to options

Answer 1

Considering we have some kind of film that produces a viscous force in opposite direction.

Let coefficient of viscosity be = N

Thus, force  = ( Formula to use in case of viscous situations)

dF = N(area)(dv/dr)  

Considering a ring of dr width of radius r

DF = N ( 2πr×dr) (wr/thickness of film )

Torque produced is     (Df)(r)

Torque is ∫ kr³

Limits of 0 to r

The torque will be proportional to R^4