In the figure shown for gives values of $R_1$ and $R_2$ the balance point for Jockey is at $40\,cm$ from $A$. When $R_2$ is shunted by a resistance of $10\, \Omega$ , balance shifts to $50\,cm.$ $R_1$ and $R_2$ are $(AB = 1 \,m)$

In a meter bridge experiment $\mathrm{S}$ is a standard resistance. $\mathrm{R}$ is a resistance wire. It is found that balancing length is $l=25 \;\mathrm{cm} .$ If $\mathrm{R}$ is replaced by a wire of half length and half diameter that of $\mathrm{R}$ of same material, then the balancing distance $\left.l^{\prime} \text { (in } \mathrm{cm}\right)$ will now be

$STATEMENT-1$ In a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance. and

$STATEMENT-2$ Resistance of a metal increases with increase in temperature.

Explain how value of unknown resistor can be obtained by using meter bridge.

A meter bridge is set up as shown, to determine an unknown resistance ' $X$ ' using a standard $10\,ohm$ resistor. The galvanometer shows null point when tapping-key is at $52\,cm$ mark. The endcorrections are $1\,cm$ and $2\,cm$ respectively for the ends $A$ and $B$. The determined value of ' $X$ ' is $……….\Omega$