The density of a material in SI units is 128 kg m^–3 . In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is -

A magnet of total magnetic moment 10^-2 $${\widehat i}$$ A-m² is placed in a time varying magnetic field, B$${\widehat i}$$ (cos $$\omega t$$) where B = 1 Tesla and $$\omega $$ = 0.125 rad/s. The work done for reversing the direction of the magnetic moment at t = 1 second, is -

In the cube of side ‘a’ shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be -

Two electric dipoles, A, B with respective dipole moments $${\overrightarrow d _A} = - 4qai$$ and $${\overrightarrow d _B} = - 2qai$$ are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both of them produce the same potential is -