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

A planar mechanism has 8 links and 10 rotary joints. The number of degrees of freedom of the mechanism, using Gruebler's criterion, is

The natural frequency of the spring mass system shown in the figure is closest to

A uniform rigid rod of mass $$m =1kg$$ and length $$L=1$$ m is hinged at its centre & laterally supported at one end by a spring of spring constant $$k=300N/m.$$ The natural frequency $${\omega _n}$$ in rad/s is