A simply supported beam $$PQ$$ is loaded by a moment of $$1$$ $$kN-m$$ at the mid-span of the beam as shown in the figure. The reaction forces $${R_P}$$ and $${R_Q}$$ at supports $$P$$ and $$Q$$ respectively are

A column has a rectangular cross-section of 10 mm $$ \times $$ 20 mm and a length of 1 m. The slenderness ratio of the column is close to

A torque $$T$$ is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. The shear modulus of the material of the rod is $$G.$$ The expressions for diameter to produce an angular twist $$\theta $$ at the free end is

For the four - bar linkage shown in the figure, the angular velocity of link AB is $$1$$ rad/s. The length of link CD is $$1.5$$ times the length of link $$AB$$. In the configuration shown, the angular velocity of link CD in rad/s is