The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement $$(x)$$ starting from mean position to extreme position (A) is given by

A parallel plate capacitor of capacitance $$2 \mathrm{~F}$$ is charged to a potential $$\mathrm{V}$$, The energy stored in the capacitor is $$E_{1}$$. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is $$\mathrm{E}_{2}$$. The ratio $$\mathrm{E}_{2} / \mathrm{E}_{1}$$ is :

The electric field in an electromagnetic wave is given as

$$\overrightarrow{\mathrm{E}}=20 \sin \omega\left(\mathrm{t}-\frac{x}{\mathrm{c}}\right) \overrightarrow{\mathrm{j}} \mathrm{NC}^{-1}$$

where $$\omega$$ and $$c$$ are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of $$5 \times 10^{-4} \mathrm{~m}^{3}$$ will be

(Given $$\varepsilon_{0}=8.85 \times 10^{-12} \mathrm{C}^{2} / \mathrm{Nm}^{2}$$ )

An average force of $$125 \mathrm{~N}$$ is applied on a machine gun firing bullets each of mass $$10 \mathrm{~g}$$ at the speed of $$250 \mathrm{~m} / \mathrm{s}$$ to keep it in position. The number of bullets fired per second by the machine gun is :