The potential energy of a particle varies with distance $x$ from a fixed origin as $U\, = \,\frac{{A\sqrt x }}{{{x^2} + B}}$ Where $A$ and $B$ are dimensional constants then find the dimensional formula for $A/B$

  • A

    ${M^2}{L^1}{T^{ - 2}}$

  • B

    ${M^1}{L^{3/2}}{T^{ - 2}}$

  • C

    ${M^0}{L^{1/5}}{T^{ - 3}}$

  • D

    ${M^2}{L^{2/2}}{T^{ - 3}}$

Similar Questions

A force $F$ is given by $F = at + b{t^2}$, where $t$ is time. What are the dimensions of $a$ and $b$

Match List $I$ with List $II$ and select the correct answer using the codes given below the lists :

List $I$ List $II$
$P.$ Boltzmann constant $1.$ $\left[ ML ^2 T ^{-1}\right]$
$Q.$ Coefficient of viscosity $2.$ $\left[ ML ^{-1} T ^{-1}\right]$
$R.$ Planck constant $3.$ $\left[ MLT ^{-3} K ^{-1}\right]$
$S.$ Thermal conductivity $4.$ $\left[ ML ^2 T ^{-2} K ^{-1}\right]$

Codes: $ \quad \quad P \quad Q \quad R \quad S $ 

  • [IIT 2013]

The equation of state of some gases can be expressed as $\left( {P + \frac{a}{{{V^2}}}} \right) = \frac{{b\theta }}{l}$ Where $P$ is the pressure, $V$ the volume, $\theta $ the absolute temperature and $a$ and $b$ are constants. The dimensional formula of $a$ is

  • [AIPMT 1996]

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]

Which of the following is dimensionally correct