Two wires $A$ and $B$ of equal lengths are connected in the left and right gaps of a metre bridge. The null point is obtained at $40 \ cm$ from the left end. If the diameters of the wires $A$ and $B$ are in the ratio $3:1$,what is the ratio of the specific resistance (resistivity) of $A$ to that of $B$ (in $:$)?

The resistances in the two arms of a meter bridge are $5\,\Omega$ and $R\,\Omega$,respectively. When the resistance $R$ is shunted with an equal resistance,the new balance point is at $1.6\,l_1$. The resistance $R$ is ................. $\Omega$.

The resistance per centimeter of a meter bridge wire is $r$. $A$ resistance of $X \ \Omega$ is placed in the left gap and a resistance of $25 \ \Omega$ is placed in the right gap. The balancing length from the left end is $40 \ cm$. Now,the wire is replaced by another wire of $2r$ resistance per centimeter. The new balancing length for the same settings will be at: (in $cm$)

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

In the meter bridge experiment,for given values of $R_1$ and $R_2$,the balance point is $20 \ cm$ from point $A$. When $R_2$ is shunted by a $20 \ \Omega$ resistance,the balancing point shifts to $50 \ cm$ from point $A$. Find the value of $R_2$ in $\Omega$.

In a meter bridge experiment, the balance point from the left is $37.5 \ cm$. The ratio of the right gap resistance to the left gap resistance is