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A cube of edge length 'a' and density 'rho' slides down a fixed inclined plane (inclined at angle theta) at a steady velocity 'v'. Between the cube's lower face and the incline there is a thin layer of viscous liquid of thickness 't'. The coefficient of viscosity of this liquid layer is:

1. 3*rho*a*g*t/(5v)
2. 4*rho*a*g*t/(5v)
3. rho*a*g*t/v
4. none of these

Correct answer: none of these

Solution

Terminal (steady) velocity means acceleration is zero, so the component of weight down the slope is balanced by the viscous shear force on the bottom film. The answer therefore depends on the incline angle theta, which the listed simple expressions do not contain, so the general result is 'none of these' unless a specific angle is given.

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