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 $A/B$
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
If $L$ and $R$ are respectively the inductance and resistance, then the dimensions of $\frac{R}{L}$ will be
If $L$ and $R$ are respectively the inductance and resistance, then the dimensions of $\frac{R}{L}$ will be
The dimensional formula of relative density is
The dimensional formula of relative density is
$\left(P+\frac{a}{V^2}\right)(V-b)=R T$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^2}{a}$, will be
$\left(P+\frac{a}{V^2}\right)(V-b)=R T$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^2}{a}$, will be
- [JEE MAIN 2023]
The dimension of $\frac{1}{2} \varepsilon_0 E ^2$, where $\varepsilon_0$ is permittivity of free space and $E$ is electric field, is
The dimension of $\frac{1}{2} \varepsilon_0 E ^2$, where $\varepsilon_0$ is permittivity of free space and $E$ is electric field, is
- [AIIMS 2014]
Why concept of dimension has basic importance ?
Why concept of dimension has basic importance ?