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A circular disc of a diameter 'd' slowly...

A circular disc of a diameter `'d'` slowly rotated in a liquid of large viscosity `'eta'` at a small distance `'h'` from a fixed surface as shown in figure. If an expression for torque `'tau'` necessary to maintain an angular velocity `'omega'` is `(pietad^(4))/(lambdah)` then fidn `lambda`.

Text Solution

Verified by Experts

The correct Answer is:
`32`
`dt = eta(2pirdr(omegar)/(h))`
`t = overset(r)underset(0)(int) (eta)/(h)2piomegar^(3)dr rArr t = int_(0)^(d//2)(etaomega)/(h)2pir^(3)dr`
`t = [(2pietaomega)/(h)(r^(4))/(4)]_(0)^(d//2) rArr t = (2pietaomega)/(h) (d^(4))/(4 xx 16)`
`t = ((pietaomegad^(4))/(32h))`
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