A differential equation of the form $${{dy} \over {dx}} = f\left( {x,y} \right)\,\,$$ is homogeneous if the function $$f(x,y)$$ depends only on the ratio $${y \over x}$$ (or) $${x \over y}$$

A spring scale indicates a tension $$T$$ in the right hand cable of the pulley system shown in figure below. Neglecting the mass of the pulleys and ignoring friction between the cable and pulley the mass $$m$$ is

A fluid is said to be Newtonian fluid when the shear stress is

The velocity components in the $$x$$ and $$y$$ directions are given by $$u = \lambda x{y^3} - {x^2}y,$$ $$v = x{y^2} - {3 \over 4}{y^4}.$$ The value of $$\lambda $$ for a possible flow field involving an incompressible fluid is