Question

A cubical block of side ${}^{\prime }{a}^{\prime }$ and denisty ${}^{\prime }{\rho }^{\prime }$ slides over a fixed inclined plane with constant velocity ${}^{\prime }{v}^{\prime }$. There is a thin film of viscous fluid of thickness ${}^{\prime }{t}^{\prime }$ between the plane and the block. Then the coefficient of viscosity of thin film will be

• A. $\frac{3\rho agt}{5v}$
• B. $\frac{4\rho agt}{5v}$
• C. $\frac{\rho agt}{v}$
• D. None of these

Answer 1

The correct option is A $\frac{3\rho agt}{5v}$


We know that, viscous force acting on block, $F_v=\eta A\frac{dv}{dy}$
Balancing forces along the incline, we get
$\eta a^2\frac{v}{t}=mg\sin {37}^{\circ }$
$\Rightarrow \eta a^2\frac{v}{t}=\rho a^{3}g.\frac{3}{5}$
$\Rightarrow \eta =\frac{3\rho agt}{5v}$