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The force is given in terms of time ‘t’ and displacement ‘x’ by the equation $F = A c o s B t + C s i n D x$ then the dimensions of ABCD is

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$[M^{2} {LT}^{-5}]$

$[{MLT}^{-5}]$

$[M^{2} L^{2} T^{-5}]$

$[M^{2} L^{3} T^{-5}]$

answer is A.

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Detailed Solution

$Bt=1 \Rightarrow B= \frac{1}{T} {=T}^{-1}$

$Dx=1 \Rightarrow D= \frac{1}{x} = \frac{1}{L} {=L}^{-1}$

$F=A \Rightarrow {MLT}^{-2} =A$

$F=C \Rightarrow {MLT}^{-2} =C$

$∴ {ABCD=MLT}^{-2} ({MLT}^{-2}) T^{-1} L^{-1} {=M}^{2} {LT}^{-5}$

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