A tube of length $$50 \mathrm{~cm}$$ is filled completely with an incompressible liquid of mass $$250 \mathrm{~g}$$ and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity $$x \sqrt{F} \,\mathrm{rad} \,\mathrm{s}^{-1}$$. If $$\mathrm{F}$$ be the force exerted by the liquid at the other end then the value of $$x$$ will be __________.

A metal wire of length $$0.5 \mathrm{~m}$$ and cross-sectional area $$10^{-4} \mathrm{~m}^{2}$$ has breaking stress $$5 \times 10^{8} \,\mathrm{Nm}^{-2}$$. A block of $$10 \mathrm{~kg}$$ is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be _________ $$\mathrm{ms}^{-1}$$.

The velocity of a small ball of mass $$0.3 \mathrm{~g}$$ and density $$8 \mathrm{~g} / \mathrm{cc}$$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $$1.3 \mathrm{~g} / \mathrm{cc}$$, then the value of viscous force acting on the ball will be $$x \times 10^{-4} \mathrm{~N}$$, The value of $$x$$ is _________. [use $$\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right]$$

The speed of a transverse wave passing through a string of length $$50 \mathrm{~cm}$$ and mass $$10 \mathrm{~g}$$ is $$60 \mathrm{~ms}^{-1}$$. The area of cross-section of the wire is $$2.0 \mathrm{~mm}^{2}$$ and its Young's modulus is $$1.2 \times 10^{11} \mathrm{Nm}^{-2}$$. The extension of the wire over its natural length due to its tension will be $$x \times 10^{-5} \mathrm{~m}$$. The value of $$x$$ is __________.