B M Sharma Solutions for Chapter: Dimensions and Measurement, Exercise 53: Exercises

Suppose two students are trying to make a new measurement system so that they can use it like a code measurement system and others do not understand it. Instead of taking $1 \mathrm{kg}, 1 \mathrm{m}$ and $1 \mathrm{s}$ as basic units, they took unit of mass as $\alpha$ $\mathrm{kg}$, the unit of length as $\beta$ $\mathrm{m}$ and unit of time as $\gamma$ $\mathrm{s}$. They called power in the new system as $\mathrm{ACME}$. Then match the two columns.

Match column $\mathrm{I}$ with column $\mathrm{II}$ and mark the correct option from the given codes. Some physical quantities are given in column $\mathrm{I}$ and some $\mathrm{SI}$ units in which these quantities may be expressed are given in column $\mathrm{II}$. Match the physical quantities in column $\mathrm{II}$ and select the code.

If volume is written as, $V\mathit{=}k{G}^x{c}^y{h}^z$. Here, $k$ is dimensionless constant and $G\text{,} c\text{,} h$ are gravitational constant, speed of light and Planck's constant, respectively. Find the value of $\frac{x}{z}$.

Acceleration due to gravity on the surface of the earth is $g\mathit{=}\frac{GM}{R^2}$. The gravitational constant $G$ is exactly known. But percentage error in measurement of the mass of earth $M$ and radius of the earth $R$ are $1\%$. and $2\%$. Respectively. The maximum percentage error is measurement of acceleration due to gravity on the surface of the earth is $n\%$. Find the value of $n$.

During measurement of kinetic energy $T$, the percentage error in measurement of mass of particle and momentum of particle are $2\%$ and $3\%$., respectively. The percentage error in measurement of kinetic energy is $n\%$. Find the value of $n$

If $y=2.21\times 0.3$,  then find the number of significant digits in the value of $y$.

If $x=0.72+0.8+3.87-1.089$, then find number of significant digits in the value of $x$.

The main scale of a vernier calipers reads in $\mathrm{milimeter}$ and its vernier is divided into $10$ divisions which coincides with $9$ divisions of the main scale. Find the reading for shown situation in $\mathrm{mm}$.