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

The force $$F$$ needed to support the liquid of density $$d$$ and the vessel on top (fig) is