Exercise - 2

The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is $0.5 \mathrm{mm}$ and there are $50$ divisions on the circular scale. The reading on the main scale is $2.5 \mathrm{mm}$ and that on the circular scale is $20$ divisions. If the measured mass of the ball has a relative error of $2\%,$ the relative percentage error in the density is

The diameter of a cylinder is measured using Vernier calipers 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

Consider a vernier calipers in which each $1 \mathrm{cm}$ on the main scale is divided into $8$ equal to divisions and a screw gauge with $100$ divisions on its circular scale. In the vernier calipers $5$ divisions on the vernier scale coincide with $4$ divisions on the main scale and in the screw gauge, one complete rotation of the circular scale moves it by two divisions on the linear scale. Then,

In an experiment, the angles are required to be measured using an instrument. $29$ divisions of the main scale exactly coincide with $30$ divisions of the vernier scale. If the smallest division of the main scale is half-a-degree $\left(=0.5°\right),$ then the least count of the instrument is

In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance $u$ and image distance $v$, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of $45°$ with the $\mathrm{X}$-axis meets the experimental curve at $\mathrm{P}$. The coordinates of $\mathrm{P}$ will be

A screw gauge gives the following reading when used to measure the diameter of a wire. 
Main scale reading : $0 \mathrm{mm}$
Circular scale reading : $52$ divisions
Given that $1 \mathrm{mm}$on main scale corresponds to $100$ divisions of the circular scale. The diameter of wire from the above data is :

A student measured the length of a rod and wrote it as $3.50 \mathrm{cm}.$ Which instrument did he use to measure it?

A screw gauge with a pitch of $0.5 \mathrm{mm}$ and a circular scale with $50$ divisions is used to measure the thickness of a thin sheet of aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the ${45}^{\text{th }}$division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is $0.5 \mathrm{mm}$ and the ${25}^{\text{th }}$ division coincides with the main scale line?