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

The resistance of a coil for d.c. is $5 \Omega$. In a.c., the resistance will