An inextensible massless string goes over a frictionless pulley. Two weights of 100 N and 200 N are attached to the two ends of the string. The weights are released from rest, and start moving due to gravity. The tension in the string (in N) is __________ .

A rigid rod $$(AB)$$ of length $$L = \sqrt 2 $$ m is undergoing translational as well as rotational motion in the $$ x-y$$ plane (see the figure). The point $$A$$ has the velocity $${V_1} = \widehat i + 2\widehat jm/s.$$ The end $$B$$ is constrained to move only along the $x$$ direction.

The magnitude of the velocity $${V_2}$$ (in $$m/s$$) at the end $$B$ is __________

For a certain two-dimensional incompressible flow, velocity field is given by $$2xy\widehat i - {y^2}\widehat j.$$ The streamlines for this flow are given by the family of curves

Consider a fully developed steady laminar flow of an incompressible fluid with viscosity $$\mu $$ through a circular pipe of radius $$R.$$ Given that the velocity at a radial location of $$R/2$$ from the center-line of the pipe is $${U_1},$$ the shear stress at the wall is $$K\mu {U_1}/R,$$ where $$K$$ is _________________.