The anode mud in the electrolytic refining of silver contains

$A$ potentiometer wire of length $1\,m$ is connected in series with a resistance of $490\,\Omega$ and a battery of $2\,V$. If the potential gradient is $0.2\,mV/cm$,then the resistance of the potentiometer wire is ............$\Omega$. (in $.9$)

Two resistances of $400\,\Omega$ and $800\,\Omega$ are connected in series with a $6\,V$ battery of negligible internal resistance. $A$ voltmeter of resistance $10,000\,\Omega$ is used to measure the potential difference across the $400\,\Omega$ resistor. The error in the measurement of potential difference (in volts) is approximately:

$A$ non-conducting body floats in a liquid at $20^{\circ} C$ with $\frac{2}{3}$ of its volume immersed in the liquid. When the liquid temperature is increased to $100^{\circ} C$, $\frac{3}{4}$ of the body's volume is immersed in the liquid. Then the coefficient of real expansion of the liquid is (neglecting the expansion of the container of the liquid):

$A$ lens forms real and virtual images of an object,when the object is at $u_1$ and $u_2$ distances respectively. If the size of the virtual image is double that of the real image,then the focal length of the lens is (take the magnification of the real image as $m$):

$A$ cannon shell fired breaks into two equal parts at its highest point. One part retraces its path to the cannon with kinetic energy $E_1$,and the kinetic energy of the second part is $E_2$. The relation between $E_1$ and $E_2$ is: