The potential energy of a particle varies with distance $x$ from a fixed origin as $V = \frac{{A\sqrt x }}{{x + B}}$,where
$A$ and $B$ are constants. The dimensions of $AB$ are

  • [AIIMS 2017]
  • A

    $ML^{5/2} T^{-2}$

  • B

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

  • C

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

  • D

    $M^1 L^{7/2} T^{-2}$

Similar Questions

If orbital velocity of planet is given by $v = {G^a}{M^b}{R^c}$, then

Time period $T\,\propto \,{P^a}\,{d^b}\,{E^c}$  then value of $c$ is  given $p$ is pressure, $d$ is density and $E$ is energy

Stokes' law states that the viscous drag force $F$ experienced by a sphere of radius $a$, moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$, is given by $F=6 \pi \eta a v$. If this fluid is flowing through a cylindrical pipe of radius $r$, length $l$ and pressure difference of $p$ across its two ends, then the volume of water $V$ which flows through the pipe in time $t$ can be written as $\frac{V}{t}=k\left(\frac{p}{l}\right)^a \eta^b r^c$, where $k$ is a dimensionless constant. Correct values of $a, b$ and $c$ are

  • [KVPY 2017]

If the formula, $X=3 Y Z^{2}, X$ and $Z$ have dimensions of capacitance and magnetic induction. The dimensions of $Y$ in $M K S Q$ system are

  • [AIIMS 2017]

If the present units of length. time and mass $(m, s, k g)$ are changed to $100\; m, 100\; s$. $\frac{1}{10} \;k g$ then