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 dimensional formula for $A B$ is
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 dimensional formula for $A B$ is
- A
$\left[ ML ^{11/2} T ^{-2}\right]$
- B
$\left[ ML ^{7 / 2} T ^{-2}\right]$
- C
$\left[M^2 L^{9 / 2} T^{-2}\right]$
- D
$\left[ ML ^{13 / 2} T ^{-3}\right]$
Similar Questions
A beaker contains a fluid of density $\rho \, kg / m^3$, specific heat $S\, J / kg\,^oC$ and viscosity $\eta $. The beaker is filled upto height $h$. To estimate the rate of heat transfer per unit area $(Q / A)$ by convection when beaker is put on a hot plate, a student proposes that it should depend on $\eta \,,\,\left( {\frac{{S\Delta \theta }}{h}} \right)$ and $\left( {\frac{1}{{\rho g}}} \right)$ when $\Delta \theta $ (in $^oC$) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for $(Q / A)$ is
- [JEE MAIN 2015]
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 $
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]
If momentum $(P)$, area $(A)$ and time $(T)$ are taken to be fundamental quantities then energy has dimensional formula
If momentum $(P)$, area $(A)$ and time $(T)$ are taken to be fundamental quantities then energy has dimensional formula
The displacement of a progressive wave is represented by $y = A\,sin \,(\omega t - kx)$ where $x$ is distance and t is time. Write the dimensional formula of $(i)$ $\omega $ and $(ii)$ $k$.
The displacement of a progressive wave is represented by $y = A\,sin \,(\omega t - kx)$ where $x$ is distance and t is time. Write the dimensional formula of $(i)$ $\omega $ and $(ii)$ $k$.
The speed of a wave produced in water is given by $v=\lambda^a g^b \rho^c$. Where $\lambda$, g and $\rho$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $a , b$ and $c$ respectively, are
The speed of a wave produced in water is given by $v=\lambda^a g^b \rho^c$. Where $\lambda$, g and $\rho$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $a , b$ and $c$ respectively, are
- [JEE MAIN 2023]