K K Sharma Solutions for Chapter: Units and Measurement, Exercise 1: TOPICWISE QUESTIONS

The length $l$, breadth $b$ and thickness $t$ of a block of wood were measured with the help of a measuring scale. The results with the permissible errors are $l=\left(15.12\pm 0.01\right) \mathrm{cm}$, $b=\left(10.15\pm 0.01\right) \mathrm{cm}$ and $t=\left(5.28\pm 0.01\right) \mathrm{cm}$. The percentage error in its volume up to $2$ proper figures is

In an experiment, the angles are required to be measured using an instrument. $29$ divisions of the main scale exactly coincide with the $30$ 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, 

The main scale of a vernier caliper reads in $\mathrm{millimetre}$ and its vernier is divided into $10$ divisions which coincides with $9$ divisions of the main scale. The reading for the shown situation is found to be $\frac{12x}{10} \mathrm{mm}$. Find the value of $x$.

The circular scale of a micrometre has $200$ divisions and a pitch of $2 \mathrm{mm}$. Find the measured value of the thickness of a thin sheet.

A travelling microscope has a main scale graduated in $\frac{1}{2} \mathrm{mm}$. $50$ vernier divisions coincide with $49$ main scale divisions. What will be the reading if the main scale reads $7.45 \mathrm{cm}$ and the ${29}^{\mathrm{th}}$ division of the vernier coincides with the main scale division?

In a screw gauge, five complete rotations of a circular scale gives $1.5 \mathrm{mm}$ reading on linear scale. The circular scale have $50$ divisions. The least count of the screw gauge is, 

A screw gauge has a screw having $2$ threads in $1 \mathrm{mm}$. The circular scale have $50$ divisions. Find the diameter of wire if the main scale shows $6^{\mathrm{th}}$ division and the vernier reads $46$.

A vernier caliper have $20$ divisions on the vernier scale which coincide with $19$ divisions on the main scale. The least count of the instrument is $0.1 \mathrm{mm}$. The main scale divisions are of