The force is given in terms of time t and displacement x by the...

The force is given in terms of time $t$ and displacement $x$ by the equation $F = AcosBx + CsinDt$

The dimensional formula of $\dfrac{AD}{B}$ is:

Options

A $\left[{M}^{0}L{T}^{- 1}\right]$
B $\left[{ML}^{2}{T}^{- 3}\right]$
C $\left[{M}^{1}{L}^{1}{T}^{- 2}\right]$
D $\left[{M}^{2}{L}^{2}{T}^{- 3}\right]$

Correct answer

B. $\left[{ML}^{2}{T}^{- 3}\right]$

Step-by-step solution

$[ A ] = \left[{MLT}^{- 2}\right]$

$[ B ] = \left[{L}^{- 1}\right]$

$[ D ] = \left[{T}^{- 1}\right]$

\left[\dfrac{AD}{B}\right] = \dfrac{\left[{MLT}^{- 2}\right]\left[{T}^{- 1}\right]}{\left[{L}^{- 1}\right]} $</p><p>\left[\dfrac{AD}{B}\right] = \left[{ML}^{2}{T}^{- 3}\right]$

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