In an experiment, the focal length of a concave mirror on a graph is drawn between the magnitudes of $u$ and $v$. The graph looks like

$1 \mathrm{cm}$ on the main scale of vernier calipers is divided into $10$ equal parts. If $10$ divisions of vernier coincide with $8$ small divisions of the main scale, then the least count of the caliper is

The end correction of a resonance tube is $1 \mathrm{cm}$. If shortest resonating length is $15 \mathrm{cm}$, the next resonating length will be

In an experiment to determine the specific heat of aluminium, piece of aluminium weighing $500 \mathrm{g}$ is heated to $100°\mathrm{C}$. It is then quickly transferred into a copper calorimeter of mass $500 \mathrm{g}$ containing $300 \mathrm{g}$ of water at$30°\mathrm{C}$. The final temperature of the mixture is found to be $46.8 °\mathrm{C}$. If specific heat of copper is $0.093 \frac{ \mathrm{cal}}{ \mathrm{g}-°\mathrm{C}}$, then the specific heat of aluminium is

The resistance in the left and right gaps of a balanced meter bridge are ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$. The balanced point is $50 \mathrm{cm}$. If a resistance of $24 \mathrm{\Omega }$ is connected in parallel to ${\mathrm{R}}_2$, the balance point is $70 \mathrm{cm}$. The value of ${\mathrm{R}}_1$ is

In a meter bridge experiment, null point is obtained at $20 \mathrm{cm}$ from one end of the wire when resistance $\mathrm{X}$ is balanced against another resistance $\mathrm{Y}$. If $\mathrm{X}<\mathrm{Y}$, then the new position of the null point from the same end, if one decides to balance a resistance of $4\mathrm{X}$ against $\mathrm{Y}$ will be at 

The distance moved by the screw of a screw gauge is $2 \mathrm{mm}$ in four rotations and there are $50$ divisions on its cap. When nothing is put between its jaws, ${20}^{\mathrm{th}}$ division of circular scale coincides with reference line, and zero of linear scale is hidden from circular scale when two jaws touch each other or zero of circular scale is lying above the reference line. When plate is placed between the jaws, main scale reads $2$ divisions and circular scale reads $20$ divisions. Thickness of plate is