If we use permittivity $ \varepsilon $, resistance $R$, gravitational constant $G$ and voltage $V$ as fundamental physical quantities, then
If we use permittivity $ \varepsilon $, resistance $R$, gravitational constant $G$ and voltage $V$ as fundamental physical quantities, then
- A
[angular displacement] $= \varepsilon^0R^0G^0V^0$
- B
[Velocity] = $\varepsilon ^{-1}R^{-1}G^0V^0$
- C
[force] = $ \varepsilon ^1R^0G^0V^2$
- D
all of the above
Similar Questions
A dimensionally consistent relation for the volume $V$ of a liquid of coefficient of viscosity $\eta $ flowing per second through a tube of radius $r$ and length $l$ and having a pressure difference $p$ across its end, is
A dimensionally consistent relation for the volume $V$ of a liquid of coefficient of viscosity $\eta $ flowing per second through a tube of radius $r$ and length $l$ and having a pressure difference $p$ across its end, is
If orbital velocity of planet is given by $v = {G^a}{M^b}{R^c}$, then
If orbital velocity of planet is given by $v = {G^a}{M^b}{R^c}$, then
If the time period $t$ of the oscillation of a drop of liquid of density $d$, radius $r$, vibrating under surface tension $s$ is given by the formula $t = \sqrt {{r^{2b}}\,{s^c}\,{d^{a/2}}} $ . It is observed that the time period is directly proportional to $\sqrt {\frac{d}{s}} $ . The value of $b$ should therefore be
- [JEE MAIN 2013]
Match List$-I$ with List$-II$
List$-I$
List$-II$
$(a)$ $h$ (Planck's constant)
$(i)$ $\left[ M L T ^{-1}\right]$
$(b)$ $E$ (kinetic energy)
$(ii)$ $\left[ M L ^{2} T ^{-1}\right]$
$(c)$ $V$ (electric potential)
$(iii)$ $\left[ M L ^{2} T ^{-2}\right]$
$(d)$ $P$ (linear momentum)
$( iv )\left[ M L ^{2} I ^{-1} T ^{-3}\right]$
Choose the correct answer from the options given below
Match List$-I$ with List$-II$
| List$-I$ | List$-II$ |
| $(a)$ $h$ (Planck's constant) | $(i)$ $\left[ M L T ^{-1}\right]$ |
| $(b)$ $E$ (kinetic energy) | $(ii)$ $\left[ M L ^{2} T ^{-1}\right]$ |
| $(c)$ $V$ (electric potential) | $(iii)$ $\left[ M L ^{2} T ^{-2}\right]$ |
| $(d)$ $P$ (linear momentum) | $( iv )\left[ M L ^{2} I ^{-1} T ^{-3}\right]$ |
Choose the correct answer from the options given below
- [JEE MAIN 2021]
Let us consider an equation
$\frac{1}{2} m v^{2}=m g h$
where $m$ is the mass of the body. velocity, $g$ is the acceleration do gravity and $h$ is the height. whether this equation is dimensionally correct.
Let us consider an equation
$\frac{1}{2} m v^{2}=m g h$
where $m$ is the mass of the body. velocity, $g$ is the acceleration do gravity and $h$ is the height. whether this equation is dimensionally correct.