Consider a truss $$PQR$$ loaded at $$P$$ with a force $$F$$ as shown in the figure. The tension in the member $$QR$$ is

A straight rod length $$L(t),$$ hinged at one end freely extensible at the other end, roates through an angle $$\theta \left( t \right)$$ about the hinge. At time $$t,$$ $$L(t)=1m,$$ $$L(t)=1m/s,$$ $$\theta \left( t \right) = \pi /4$$ rad and $$\mathop \theta \limits^ \cdot \left( t \right) = 1\,\,rad/s.$$ The magnitude of the velocity at the other end of the rod is

A two dimensional fluid element rotates like a rigid body. At a point with in the element, the pressure is $$1$$ unit. Radius of the Mohr's circle, charactering the state of stress at the point, is

The gap between a moving circular plate and a stationary surface is being continuously reduced, as the circular plate comes down at a uniform speed $$V$$ towards the stationary bottom surface, as shown in the figure. In the process, the fluid contained between the two plates flows out radially. The fluid is assumed to be incompressible and inviscid.

The radial velocity $${V_r},$$ at any radius $$r$$, when the gap width is $$h,$$ is