The diameter of a cylinder is measured using a vernier callipers with no zero error. It is found that the zero of the vernier scale lies between $5.10 \mathrm{cm}$ and $5.15 \mathrm{cm}$ of the main scale. The vernier scale has $50$  divisions equivalent to $2.45 \mathrm{cm}$. The ${24}^{\mathrm{th}}$ division of the vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is, 

In order to measure the internal resistance $r_1$ of a cell of emf $\epsilon ,$ a meter bridge of wire resistance $R_0=50 \mathrm{\Omega }$, a resistance $\frac{R_0}{2}$, another cell of emf $\frac{\epsilon }{2}$ (internal resistance $r$) and a galvanometer $G$ are used in a circuit, as shown in the figure. If the null point is found at $l=72 \mathrm{cm},$ then the value of $r_1=\_\_\_\_\mathrm{\Omega }.$

There are two vernier calipers both of which have $1 \mathrm{cm}$ divided into $10$ equal divisions on the main scale. The Vernier scale of one of the calipers $\left(C_1\right)$ has $10$ equal divisions that correspond to $9$ main scale divisions. The Vernier scale of the other caliper $\left(C_2\right)$ has $10$ equal divisions that correspond to $11$ main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in $\mathrm{cm}$) by calipers $C_1$ and $C_2$ respectively, are

During an experiment with a metre bridge, the galvanometer shows a null point when the jockey is pressed at $40.0 \mathrm{cm }$using a standard resistance of $90\mathrm{ }\mathrm{\Omega }$ ,as shown in the figure. The least count of the scale used in the metre bridge is $1\mathrm{mm}$. The unknown resistance is

The smallest division on the main scale of a Vernier calipers is $0.1 \mathrm{cm}$. Ten divisions of the Vernier scale correspond to nine divisions of the main scale. The figure below on the left shows the reading of this calipers with no gap between its two jaws. The figure on the right shows the reading with a solid sphere held between the jaws. The correct diameter of the sphere is