A dimensionless quantity is constructed in terms of electronic charge $e$, permittivity of free space $\varepsilon_0$, Planck's constant $h$, and speed of light $c$. If the dimensionless quantity is written as $e^\alpha \varepsilon_0^\beta h^7 c^5$ and $n$ is a non-zero integer, then $(\alpha, \beta, \gamma, \delta)$ is given by
IIT 2024, Easy
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1View SolutionDimensions of pair are same. Identify the pair
- 2What is the number of significant figures in $11.118 \times 10^{ - 6}\,V$View Solution
- 3The radius ( $\mathrm{r})$, length $(l)$ and resistance $(\mathrm{R})$ of a metal wire was measured in the laboratory asView Solution
$\mathrm{r}=(0.35 \pm 0.05) \mathrm{cm}$
$\mathrm{R}=(100 \pm 10) \mathrm{ohm}$
$l=(15 \pm 0.2) \mathrm{cm}$
The percentage error in resistivity of the material of the wire is :
- 4Time period $T\,\propto \,{P^a}\,{d^b}\,{E^c}$ then value of $c$ is given $p$ is pressure, $d$ is density and $E$ is energyView Solution
- 5View SolutionDimensions of magnetic field intensity is
- 6A screw gauge gives the following reading when used to measure the diameter of a wire.View Solution
Main scale reading : $0\ mm$
Circular scale reading : $52\ divisions$
Given that $1\ mm$ on main scale corresponds to $100$ divisions of the circular scale. The diameter of wire from the above data is:
- 7View SolutionThe pair(s) of physical quantities that have the same dimensions, is (are)
- 8View Solutionwhich of the following is not an unit of Length?
- 9Consider following statementsView Solution
$(A)$ Any physical quantity have more than one unit
$(B)$ Any physical quantity have only one dimensional formula
$(C)$ More than one physical quantities may have same dimension
$(D)$ We can add and subtract only those expression having same dimension
Number of correct statement is
- 10In a system of units if force $(F)$, acceleration $(A) $ and time $(T)$ are taken as fundamental units then the dimensional formula of energy isView Solution