If the pressure at half the depth of a lake is equal to $2/3$ of the pressure at the bottom of the lake,then what is the depth of the lake in $m$? (Assume atmospheric pressure $P_0 = 10^5 \ Pa$,density of water $\rho = 10^3 \ kg/m^3$,and $g = 10 \ m/s^2$)

The acceleration due to gravity is measured on the surface of the Earth by using a simple pendulum. If $\alpha$ and $\beta$ are relative errors in the measurement of length and time period respectively,then the percentage error in the measurement of acceleration due to gravity is ................

The circumcentre of the triangle with vertices at $(-2, 3)$,$(1, -2)$ and $(2, 1)$ is

The calculated magnetic moment (in Bohr magnetons) of $Cu^{2+}$ ion is

The electric field of a plane electromagnetic wave varies with time with an amplitude of $2 \, Vm^{-1}$ propagating along the $z$-axis. The average energy density of the magnetic field (in $J \, m^{-3}$) is:

In the $Hoop$ process for the refining of $Al$,the molten materials form three different layers and remain separate during electrolysis because ..........