A bob of simple pendulum of mass 'm' perform $$\mathrm{SHM}$$ with amplitude '$$\mathrm{A}$$' and period 'T'. Kinetic energy of pendulum of displacement $$x=\frac{A}{2}$$ will be

Two positive ions, each carrying a charge 'q' are separated by a distance 'd'. If 'F' is the force of repulsion between the ions, the number of electrons from each ion will be ($$\varepsilon$$ = charge on $$\varepsilon_k$$ = permittivity of free space)

Two circular loops P and Q are made from a uniform wire. The radii of P and Q are R$$_1$$ and R$$_2$$ respectively. The momentsw of inertia about their own axis are $$\mathrm{I_P}$$ and $$\mathrm{I_Q}$$ respectively. If $$ \frac{\mathrm{I}_{\mathrm{P}}}{\mathrm{I}_Q}=\frac{1}{8}$$ then $$\mathrm{\frac{R_2}{R_1}}$$ is

A metre scale is supported on a wedge at its centre of gravity. A body of weight 'w'. is suspended from the $$20 \mathrm{~cm}$$ mark and another weight of 25 gram is suspended from $$74 \mathrm{~cm}$$ mark balance it and the metre scale remains perfectly horizontal. Neglecting the weight of the metre scale, the weight of the body is