Two spherical conductors each of capacity $C$ are charged to potentials $V$ and $-V$. These are then connected by means of a fine conducting wire. The loss of energy will be

$A$ vertical spring with force constant $k$ is fixed on a table. $A$ ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is

In the equation $\log S = \log C + Z \log A$,what does '$C$' represent?

There are two holes,one each along the opposite sides of a wide rectangular tank. The cross-section of each hole is $0.01 ~m^2$ and the vertical distance between the holes is $1 ~m$. The tank is filled with water. The net force on the tank in newtons when the water flows out of the holes is (Density of water $= 1000 ~kg/m^3$,$g = 10 ~m/s^2$):

The truth table for the system of four $NAND$ gates as shown in the figure is:

$A$ straight line $L$ at a distance of $4$ units from the origin makes positive intercepts on the coordinate axes,and the perpendicular drawn from the origin to this line makes an angle of $60^{\circ}$ with the line $x+y=0$. Then the equation of the line $L$ is