The bob of a simple pendulum of length '$$L$$' has a mass '$$\mathrm{m}$$' and charge '$$\mathrm{q}$$'. The pendulum is suspended between the plates of a charged parallel plate capacitor. The direction of electric field is shown in figure. The period of oscillations of the simple pendulum is (acceleration due to gravity $$\mathrm{g}>\mathrm{qE} / \mathrm{m}$$ )

An electron is projected along the axis of circular conductor carrying current I. Electron will experience

Two identical capacitors have the same capacitance '$$C$$'. One of them is charged to a potential $$V_1$$ and the other to $$V_2$$. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is

A transverse wave $$\mathrm{Y}=2 \sin (0.01 \mathrm{x}+30 \mathrm{t})$$ moves on a stretched string from one end to another end in 0.5 second. If $$x$$ and $$y$$ are in $$\mathrm{cm}$$ and $$t$$ in second, then the length of the string is