The distance between two plates of a capacitor is $$\mathrm{d}$$ and its capacitance is $$\mathrm{C}_{1}$$, when air is the medium between the plates. If a metal sheet of thickness $$\frac{2 d}{3}$$ and of the same area as plate is introduced between the plates, the capacitance of the capacitor becomes $$\mathrm{C}_{2}$$. The ratio $$\frac{\mathrm{C}_{2}}{\mathrm{C}_{1}}$$ is

A force of $$-\mathrm{P} \hat{\mathrm{k}}$$ acts on the origin of the coordinate system. The torque about the point $$(2,-3)$$ is $$\mathrm{P}(a \hat{i}+b \hat{j})$$, The ratio of $$\frac{a}{b}$$ is $$\frac{x}{2}$$. The value of $$x$$ is -

A straight wire carrying a current of $$14 \mathrm{~A}$$ is bent into a semi-circular arc of radius $$2.2 \mathrm{~cm}$$ as shown in the figure. The magnetic field produced by the current at the centre $$(\mathrm{O})$$ of the arc. is ____________ $$\times ~10^{-4} \mathrm{~T}$$

A rectangular block of mass $$5 \mathrm{~kg}$$ attached to a horizontal spiral spring executes simple harmonic motion of amplitude $$1 \mathrm{~m}$$ and time period $$3.14 \mathrm{~s}$$. The maximum force exerted by spring on block is _________ N