In a metre bridge experiment (see figure), the positions of the cell, $E$, and galvanometer, $G$, are interchanged. We shall observe in the galvanometer:

When a wire is connected in the left gap of a metre bridge,the balancing point is at $40 \ cm$ from the left end of the bridge wire. If the wire in the left gap is stretched so that its length is doubled and again connected in the same gap,then the balancing point from the left end of the bridge wire is

$A$ resistance wire connected in the left gap of a meter bridge balances a $10\, \Omega$ resistance in the right gap at a point which divides the bridge wire in the ratio $3: 2$. If the length of the resistance wire is $1.5\, m$,then the length of $1\, \Omega$ of the resistance wire is $....... \times 10^{-2}\, m$.

$A$ resistance of $2\,\Omega$ is connected across one gap of a meter-bridge and an unknown resistance,greater than $2\,\Omega$,is connected across the other gap. When these resistances are interchanged,the balance point shifts by $20\,cm$. Neglecting any end correction,the unknown resistance is ................ $\Omega$.

Two resistors $2 \Omega$ and $3 \Omega$ are connected in the gaps of a meter bridge as shown in the figure. The null point is obtained with the contact of the jockey at some point on the wire $XY$. When an unknown resistor $R$ is connected in parallel with the $3 \Omega$ resistor, the null point is shifted by $22.5 \text{ cm}$ toward $Y$. The resistance of the unknown resistor $R$ is . . . . . . $\Omega$.

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