A simple pendulum performs simple harmonic motion about $$\mathrm{x}=0$$ with an amplitude '$$\mathrm{a}$$' and time period '$$T$$'. The speed of the pendulum at $$x=\frac{a}{2}$$ is

The molar specific heat of an ideal gas at constant pressure and constant volume is $$\mathrm{C}_{\mathrm{p}}$$ and $$\mathrm{C}_{\mathrm{v}}$$ respectively. If $$\mathrm{R}$$ is universal gas constant and $$\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}$$ then $$\mathrm{C}_{\mathrm{v}}=$$

Resistance of a potentiometer wire is $$2 \Omega / \mathrm{m}$$. A cell of e.m.f. $$1.5 \mathrm{~V}$$ balances at $$300 \mathrm{~cm}$$. The current through the wire is

$$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$ are three parallel conductors of equal lengths and carry currents I, I and 2I respectively as shown in figure. Distance $$A B$$ and $$B C$$ is same as '$$d$$'. If '$$F_1$$' is the force exerted by $$\mathrm{B}$$ on $$\mathrm{A}$$ and $$\mathrm{F}_2$$ is the force exerted by $$\mathrm{C}$$ on $$\mathrm{A}$$, then