The oxide of a metal contains $40 \%$ of oxygen. The valency of the metal is $2$. What is the atomic weight of the metal?

$A$ particle executes $SHM$ on a straight line path. The amplitude of oscillation is $2 \, cm$. When the displacement of the particle from the mean position is $1 \, cm$,the numerical value of the magnitude of acceleration is equal to the numerical value of the magnitude of velocity. The frequency of $SHM$ is (in $s^{-1}$):

Water is filled up to a height $h$ in a beaker of radius $R$ as shown in the figure. The density of water is $\rho$,the surface tension of water is $T$ and the atmospheric pressure is $P_0$. Consider a vertical section $ABCD$ of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude

$\log _4 2 - \log _8 2 + \log _{16} 2 - \dots$ is equal to

What is the equivalent capacitance of the system of capacitors between $A$ and $B$?

$A$ mercury drop of radius $1 ~cm$ is sprayed into $10^6$ drops of equal size. The energy expended in joules is (Surface tension of mercury is $460 \times 10^{-3} ~N/m$)