D. C. Pandey Solutions for Chapter: Units, Dimensions and Error Analysis, Exercise 1: Excercise 1

The force of interaction between two atoms is given by $F=\alpha \beta \exp \left(-\frac{x^2}{\alpha kT}\right)$ where $x$ is the distance, $k$ is the Boltzmann constant and $T$ is temperature and $\alpha$ and $\beta$ are two constants. The dimension of $\beta$ is

The least count of the main scale of a screw gauge is $1 \mathrm{mm}$. The minimum number of divisions on its circular scale required to measure $5 \mu \mathrm{m}$ diameter of a wire is

The dimensional formula of $\sqrt{\frac{{\mu }_0}{{\epsilon }_0}}$ is

A physical quantity obtained from the ratio of the coefficient of thermal conductivity to the universal gravitational constant has a dimensional formula $\left[{\mathrm{M}}^{2a}{\mathrm{L}}^{4b}{\mathrm{T}}^{2c}{\mathrm{K}}^d\right]$, then the value of $\frac{a+b}{c+b}-d$ is

A current carrying conductor obeys Ohm's law $\left(V=RI\right)$. If the current passing through the conductor is $I=\left(5\pm 0.2\right) \mathrm{A}$ and voltage developed is $V=\left(60\pm 6\right) \mathrm{V},$ then find the percentage of error is resistance, $R$

The force $F$ acting on a body of density $d$ are related by the relation $F=\frac{y}{\sqrt{d}}.$ The dimensions of $y$ are

The SI unit and dimensions of Stefan's constant $\sigma$ in case of Stefan's law of radiation is

The density of the material of a cube can be estimated by measuring its mass and the length of one of its sides. If the maximum error in the measurement of mass and length are $0.3\%$ and $0.2\%$ respectively, the maximum error in the estimation of the density of the cube is approximately.