The equation $\frac{{dV}}{{dt}} = At - BV$ is describing the rate of change of velocity of a body falling from rest in a resisting medium. The dimensions of $A$ and $B$ are

  • A

    $LT^{-3}, T$

  • B

    $LT^{-3}, T^{-1}$

  • C

    $LT, T$

  • D

    $LT, T^{-1}$

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  • [IIT 2015]

The dimensions of physical quantity $X$ in the equation Force $ = \frac{X}{{{\rm{Density}}}}$ is given by