Consider two physical quantities A and B related to each other as $E=\frac{B-x^2}{A t}$ where $E, x$ and $t$ have dimensions of energy, length and time respectively. The dimension of $A B$ is
Consider two physical quantities A and B related to each other as $E=\frac{B-x^2}{A t}$ where $E, x$ and $t$ have dimensions of energy, length and time respectively. The dimension of $A B$ is
- [JEE MAIN 2024]
- A
$\mathrm{L}^{-2} \mathrm{M}^1 \mathrm{~T}^0$
- B
$\mathrm{L}^2 \mathrm{M}^{-1} \mathrm{~T}^1$
- C
$\mathrm{L}^{-2} \mathrm{M}^{-1} \mathrm{~T}^1$
- D
$\mathrm{L}^0 \mathrm{M}^{-1} \mathrm{~T}^1$
Similar Questions
Which of the following is dimensionally incorrect?
Which of the following is dimensionally incorrect?
Density of wood is $0.5 \;gm / cc$ in the $CGS$ system of units. The corresponding value in $MKS$ units is.?
Force $(F)$ and density $(d)$ are related as $F\, = \,\frac{\alpha }{{\beta \, + \,\sqrt d }}$ then dimension of $\alpha $ and $\beta$ are
A force $F$ is given by $F = at + b{t^2}$, where $t$ is time. What are the dimensions of $a$ and $b$
A force $F$ is given by $F = at + b{t^2}$, where $t$ is time. What are the dimensions of $a$ and $b$
An artificial satellite is revolving around a planet of mass $M$ and radius $R$ in a circular orbit of radius $r$. From Kepler’s third law about the period of a satellite around a common central body, square of the period of revolution $T$ is proportional to the cube of the radius of the orbit $r$. Show using dimensional analysis that $T\, = \,\frac{k}{R}\sqrt {\frac{{{r^3}}}{g}} $, where $k$ is dimensionless constant and $g$ is acceleration due to gravity.
An artificial satellite is revolving around a planet of mass $M$ and radius $R$ in a circular orbit of radius $r$. From Kepler’s third law about the period of a satellite around a common central body, square of the period of revolution $T$ is proportional to the cube of the radius of the orbit $r$. Show using dimensional analysis that $T\, = \,\frac{k}{R}\sqrt {\frac{{{r^3}}}{g}} $, where $k$ is dimensionless constant and $g$ is acceleration due to gravity.