A physical quantity $\vec{S}$ is defined as $\vec{S}=(\vec{E} \times \vec{B}) / \mu_0$, where $\vec{E}$ is electric field, $\vec{B}$ is magnetic field and $\mu_0$ is the permeability of free space. The dimensions of $\vec{S}$ are the same as the dimensions of which of the following quantity (ies)?
$(A)$ $\frac{\text { Energy }}{\text { charge } \times \text { current }}$
$(B)$ $\frac{\text { Force }}{\text { Length } \times \text { Time }}$
$(C)$ $\frac{\text { Energy }}{\text { Volume }}$
$(D)$ $\frac{\text { Power }}{\text { Area }}$
A physical quantity $\vec{S}$ is defined as $\vec{S}=(\vec{E} \times \vec{B}) / \mu_0$, where $\vec{E}$ is electric field, $\vec{B}$ is magnetic field and $\mu_0$ is the permeability of free space. The dimensions of $\vec{S}$ are the same as the dimensions of which of the following quantity (ies)?
$(A)$ $\frac{\text { Energy }}{\text { charge } \times \text { current }}$
$(B)$ $\frac{\text { Force }}{\text { Length } \times \text { Time }}$
$(C)$ $\frac{\text { Energy }}{\text { Volume }}$
$(D)$ $\frac{\text { Power }}{\text { Area }}$
- [IIT 2021]
- A
$A,B,C$
- B
$A,B,D$
- C
$A,B$
- D
$B,D$
Similar Questions
Match List $I$ with List $II$
List $I$
List $II$
$A$ Spring constant
$I$ $(T ^{-1})$
$B$ Angular speed
$II$ $(MT ^{-2})$
$C$ Angular momentum
$III$ $(ML ^2)$
$D$ Moment of Inertia
$IV$ $(ML ^2 T ^{-1})$
Choose the correct answer from the options given below
Match List $I$ with List $II$
| List $I$ | List $II$ |
| $A$ Spring constant | $I$ $(T ^{-1})$ |
| $B$ Angular speed | $II$ $(MT ^{-2})$ |
| $C$ Angular momentum | $III$ $(ML ^2)$ |
| $D$ Moment of Inertia | $IV$ $(ML ^2 T ^{-1})$ |
Choose the correct answer from the options given below
- [JEE MAIN 2023]
The workdone by a gas molecule in an isolated system is given by, $W =\alpha \beta^{2} e ^{-\frac{ x ^{2}}{\alpha kT }},$ where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature, $\alpha$ and $\beta$ are constants. Then the dimension of $\beta$ will be
The workdone by a gas molecule in an isolated system is given by, $W =\alpha \beta^{2} e ^{-\frac{ x ^{2}}{\alpha kT }},$ where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature, $\alpha$ and $\beta$ are constants. Then the dimension of $\beta$ will be
- [JEE MAIN 2021]
If velocity of light $c$, Planck’s constant $h$ and gravitational constant $G$ are taken as fundamental quantities, then express mass, length and time in terms of dimensions of these quantities.
If velocity of light $c$, Planck’s constant $h$ and gravitational constant $G$ are taken as fundamental quantities, then express mass, length and time in terms of dimensions of these quantities.
If velocity$(V)$, force$(F)$ and time$(T)$ are chosen as fundamental quantities then dimensions of energy are
If velocity$(V)$, force$(F)$ and time$(T)$ are chosen as fundamental quantities then dimensions of energy are
Heat produced in a current carrying conducting wire depends on current $I$, resistance $R$ of the wire and time $t$ for which current is passed. Using these facts, obtain the formula for heat energy.
Heat produced in a current carrying conducting wire depends on current $I$, resistance $R$ of the wire and time $t$ for which current is passed. Using these facts, obtain the formula for heat energy.