If force $({F})$, length $({L})$ and time $({T})$ are taken as the fundamental quantities. Then what will be the dimension of density

  • [JEE MAIN 2021]
  • A

    $\left[{FL}^{-4} {T}^{2}\right]$

  • B

    $\left[{FL}^{-3} {T}^{2}\right]$

  • C

    $\left[{FL}^{-5} {T}^{2}\right]$

  • D

    $\left[{FL}^{-3} {T}^{3}\right]$

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  • [IIT 2004]

A calorie is a unit of heat or energy and it equals about $4.2\; J$ where $1 \;J =1\; kg \,m ^{2} \,s ^{-2}$ Suppose we employ a system of units in which the unit of mass equals $\alpha\; kg$, the unit of length equals $\beta\; m$, the unit of time is $\gamma$ $s$. Show that a calorie has a magnitude $4.2 \;\alpha^{-1} \beta^{-2} \gamma^{2}$ in terms of the new units.

If velocity $[V],$ time $[T]$ and force $[F]$ are chosen as the base quantities, the dimensions of the mass will be

  • [JEE MAIN 2021]

Which of the following is not a dimensionless quantity?

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Write the dimensions of $a/b$ in the relation $P = \frac{{a - {t^2}}}{{bx}}$ , where $P$ is pressure, $x$ is the distance and $t$ is the time