For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clamped to the case with both ends hinged is

A cantilever beam of length $$L$$ is subjected to a moment $$M$$ at the free end. The moment of inertia of the beam cross section about the neutral axis is $$I$$ and the Young’s modulus is $$E$$. The magnitude of the maximum deflection is

A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1%, with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is

In the mechanism given below, if the angular velocity of the eccentric circular disc is $$1$$ rad/s, the angular velocity (rad/s) of the follower link for the instant shown in the figure is

Note : $$All$$ $$dimensions$$ $$are$$ $$in$$ $$mm$$