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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: a)R^2 b)R^3 c)R^4 d)R^6

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:
a)R^2 b)R^3 c)R^4 d)R^6

Grade:12th pass

1 Answers

Sukhamjot Singh
9 Points
3 years ago
Considering we have some kind of film that produces viscous force in opposite direction.
Let coefficient of viscosity be N
Force
dF = N(area)(dv/dr)         [This is a popular formula dealt in viscous situations]
Considering a ring of dr width of radius r
DF = N ( 2 pi r dr) (wr/thickness of film )
Torque produced is     (Df)(r)
Torque is \int kr^3
LIMITS 0to R 
WE GET TORQUE PROPORTIONAL TO R^4

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