In an experiment with vernier callipers of least count $$0.1 \mathrm{~mm}$$, when two jaws are joined together the zero of vernier scale lies right to the zero of the main scale and 6th division of vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between $$3.2 \mathrm{~cm}$$ and $$3.3 \mathrm{~cm}$$ marks, and 4th division of vernier scale coincides with the main scale division. The diameter of bob is measured as

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 ____________ $$\times ~10^{-4} \mathrm{~T}$$