If force $(F)$, velocity $(V)$ and time $(T)$ are considered as fundamental physical quantity, then dimensional formula of density will be:

  • [JEE MAIN 2023]
  • A
    $FV ^{-2} T ^2$
  • B
    $FV ^{-4} T ^{-2}$
  • C
    $FV ^4 T ^{-6}$
  • D
    $F ^2 V ^{-2} T ^6$

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The equation of state of some gases can be expressed as $\left( {P + \frac{a}{{{V^2}}}} \right) = \frac{{b\theta }}{l}$ Where $P$ is the pressure, $V$ the volume, $\theta $ the absolute temperature and $a$ and $b$ are constants. The dimensional formula of $a$ is

  • [AIPMT 1996]

If $P$ represents radiation pressure, $c$ represents speed of light and $Q$ represents radiation energy striking a unit area per second, then non-zero integers $x,\,y$ and $z$ such that ${P^x}{Q^y}{c^z}$ is dimensionless, are

  • [AIPMT 1992]

The equation of the stationary wave is
$y = 2A\,\,\sin \,\left( {\frac{{2\pi ct}}{\lambda }} \right)\,\cos \,\,\,\left( {\frac{{2\pi x}}{\lambda }} \right)$
Which statement is not true?

In a particular system of units, a physical quantity can be expressed in terms of the electric charge $c$, electron mass $m_c$, Planck's constant $h$, and Coulomb's constant $k=\frac{1}{4 \pi \epsilon_0}$, where $\epsilon_0$ is the permittivity of vacuum. In terms of these physical constants, the dimension of the magnetic field is $[B]=[c]^\alpha\left[m_c\right]^\beta[h]^\gamma[k]^\delta$. The value of $\alpha+\beta+\gamma+\delta$ is. . . . .

  • [IIT 2022]

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]