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

A circuit containing resistance R$$_1$$, inductance L$$_1$$ and capacitance C$$_1$$ connected in series resonates at the same frequency 'f$$_0$$' as another circuit containing R$$_2$$, L$$_2$$ and C$$_2$$ in series. If two circuits are connected in series then the new frequency at resonance is

An object executes SHM along $$x$$-axis with amplitude $$0.06 \mathrm{~m}$$. At certain distance '$$\mathrm{x}$$' metre from mean position, it has kinetic energy $$10 \mathrm{~J}$$ and potential energy $$8 \mathrm{~J}$$. the distance '$$\mathrm{x}$$' will be