The mass of a liquid flowing per second per unit area of cross section of a tube is proportional to $P^x$ and $v^y$ , where $P$ is the pressure difference and $v$ is the velocity. Then, the relation between $x$ and $y$ is
The mass of a liquid flowing per second per unit area of cross section of a tube is proportional to $P^x$ and $v^y$ , where $P$ is the pressure difference and $v$ is the velocity. Then, the relation between $x$ and $y$ is
- A
$x = y$
- B
$x = -y$
- C
$x = -y^2$
- D
$y = x^2$
Similar Questions
In the expression $P = El^2m^{-5}G^{-2}$, $E$, $l$, $m$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively. Show that $P$ is a dimensionless quantity.
In the expression $P = El^2m^{-5}G^{-2}$, $E$, $l$, $m$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively. Show that $P$ is a dimensionless quantity.
Match List $I$ with List $II$
List $I$
List $II$
$A$ Torque
$I$ ${\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]}$
$B$ Magnetic fileld
$II$ $\left[\mathrm{L}^2 \mathrm{~A}^1\right]$
$C$ Magnetic moment
$III$ ${\left[\mathrm{M}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]}$
$D$ Permeability of free space
$IV$ $\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]$
Choose the correct answer from the options given below :
| List $I$ | List $II$ |
| $A$ Torque | $I$ ${\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]}$ |
| $B$ Magnetic fileld | $II$ $\left[\mathrm{L}^2 \mathrm{~A}^1\right]$ |
| $C$ Magnetic moment | $III$ ${\left[\mathrm{M}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]}$ |
| $D$ Permeability of free space | $IV$ $\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]$ |
- [JEE MAIN 2024]
If the time period $(T)$ of vibration of a liquid drop depends on surface tension $(S)$, radius $(r)$ of the drop and density $(\rho )$ of the liquid, then the expression of $T$ is
If the time period $(T)$ of vibration of a liquid drop depends on surface tension $(S)$, radius $(r)$ of the drop and density $(\rho )$ of the liquid, then the expression of $T$ is
If energy $(E),$ velocity $(V)$ and time $(T)$ are chosen as the fundamental quantities, the dimensional formula of surface tension will be
If energy $(E),$ velocity $(V)$ and time $(T)$ are chosen as the fundamental quantities, the dimensional formula of surface tension will be
- [AIEEE 2012]
The dimension of stopping potential $\mathrm{V}_{0}$ in photoelectric effect in units of Planck's constant $h$, speed of light $c$, Gravitational constant $G$ and ampere $A$ is
- [JEE MAIN 2020]