Two different coils have self - inductance $\mathrm{L}_1=9 \mathrm{mH}$ and $\mathrm{L}_2=3 \mathrm{mH}$. The current in first coil is increased at a constant rate. The current in the second coil is also increased at the same constant rate. At certain instant of time, the power given to the two coils is same. At that time, there was current and induced voltage in the two coils. At the same instant, the ratio of the energy stored in the first coil to that in second coil is
Four masses of $1 \mathrm{~kg}, 2 \mathrm{~kg}, 3 \mathrm{~kg}$ and 4 kg are kept at co-ordinates $(0,0) \mathrm{m},(0,1) \mathrm{m}$ and $(1,0) \mathrm{m}$ respectively. Using the co-ordinates of centre of mass its position vector is
In between the plates of parallel plate capacitor of plate separation 'd' a dielectric plate of thickness ' $t$ ' is inserted. The capacitance becomes one-third of the original capacity without dielectric. The dielectric constant of the plate is
A thin rod of length ' 4 L ' and mass ' 4 m ' is bent at the points as shown in the figure. The moment of inertia of the rod about an axis passing through point ' $O$ ' and perpendicular to plane of the paper is
