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 __________.

The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is $$10 \mathrm{~s}$$. If the metallic bob is immersed in water, then the new time period becomes $$5 \sqrt{x}$$ s. The value of $$x$$ will be ________.

A $$8 \mathrm{~V}$$ Zener diode along with a series resistance $$\mathrm{R}$$ is connected across a $$20 \mathrm{~V}$$ supply (as shown in the figure). If the maximum Zener current is $$25 \mathrm{~mA}$$, then the minimum value of R will be _______ $$\Omega$$.