The resistances in the two gaps of a balanced meter bridge are $X \ \Omega$ and $3X \ \Omega$ respectively. If the resistances are interchanged, the balance point shifts by: (in $\text{ cm}$)

In a meter bridge experiment,the balance point is obtained if the gaps are closed by $2\,\Omega$ and $3\,\Omega$ resistors. $A$ shunt of $x\,\Omega$ is added to the $3\,\Omega$ resistor to shift the balancing point by $22.5\,cm$. The value of $x$ is $................$

In the experimental setup of a meter bridge shown in the figure,the null point is obtained at a distance of $40\,cm$ from $A$. If a $10\,\Omega$ resistor is connected in series with $R_1$,the null point shifts by $10\,cm$. The resistance that should be connected in parallel with $(R_1 + 10)\,\Omega$ such that the null point shifts back to its initial position is .............. $\Omega$.

$A$ resistance of $2 \Omega$ is connected across one gap of a metre-bridge (the length of the wire is $100 \text{ cm}$) and an unknown resistance,greater than $2 \Omega$,is connected across the other gap. When these resistances are interchanged,the balance point shifts by $20 \text{ cm}$. Neglecting any corrections,the unknown resistance is (in $\Omega$)

In a metre bridge experiment,the ratio of the left gap resistance to the right gap resistance is $2:3$. The balance point from the left is: (in $cm$)

The unknown resistances are connected in two gaps of a metre bridge. The null point is at $20 \ cm$ from the zero end. $A$ resistance of $15 \ \Omega$ is connected in series with the smaller of the two. The null point shifts to $40 \ cm$. The smaller resistance is (in $\Omega$)