If velocity $[V],$ time $[T]$ and force $[F]$ are chosen as the base quantities, the dimensions of the mass will be
If velocity $[V],$ time $[T]$ and force $[F]$ are chosen as the base quantities, the dimensions of the mass will be
- [JEE MAIN 2021]
- A
$\left[{FT}^{-1} {V}^{-1}\right]$
- B
$[FTV$ $\left.^{-1}\right]$
- C
$\left[{FT}^{2} {V}\right]$
- D
$\left[{FVT}^{-1}\right]$
Similar Questions
A book with many printing errors contains four different formulas for the displacement $y$ of a particle undergoing a certain periodic motion:
$(a)\;y=a \sin \left(\frac{2 \pi t}{T}\right)$
$(b)\;y=a \sin v t$
$(c)\;y=\left(\frac{a}{T}\right) \sin \frac{t}{a}$
$(d)\;y=(a \sqrt{2})\left(\sin \frac{2 \pi t}{T}+\cos \frac{2 \pi t}{T}\right)$
$(a=$ maximum displacement of the particle, $v=$ speed of the particle. $T=$ time-period of motion). Rule out the wrong formulas on dimensional grounds.
A book with many printing errors contains four different formulas for the displacement $y$ of a particle undergoing a certain periodic motion:
$(a)\;y=a \sin \left(\frac{2 \pi t}{T}\right)$
$(b)\;y=a \sin v t$
$(c)\;y=\left(\frac{a}{T}\right) \sin \frac{t}{a}$
$(d)\;y=(a \sqrt{2})\left(\sin \frac{2 \pi t}{T}+\cos \frac{2 \pi t}{T}\right)$
$(a=$ maximum displacement of the particle, $v=$ speed of the particle. $T=$ time-period of motion). Rule out the wrong formulas on dimensional grounds.
In a system of units if force $(F)$, acceleration $(A) $ and time $(T)$ are taken as fundamental units then the dimensional formula of energy is
In a system of units if force $(F)$, acceleration $(A) $ and time $(T)$ are taken as fundamental units then the dimensional formula of energy is
The quantum hall resistance $R_H$ is a fundamental constant with dimensions of resistance. If $h$ is Planck's constant and $e$ is the electron charge, then the dimension of $R_H$ is the same as
The quantum hall resistance $R_H$ is a fundamental constant with dimensions of resistance. If $h$ is Planck's constant and $e$ is the electron charge, then the dimension of $R_H$ is the same as
- [KVPY 2011]
if Energy is given by $U = \frac{{A\sqrt x }}{{{x^2} + B}},\,$, then dimensions of $AB$ is
if Energy is given by $U = \frac{{A\sqrt x }}{{{x^2} + B}},\,$, then dimensions of $AB$ is
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]