Force F = P cos(Ax) + Q sin(Bt),where x and t | vedclass

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(B) In the given equation $F = P \cos(Ax) + Q \sin(Bt)$,the arguments of trigonometric functions must be dimensionless.Therefore,the dimensions of $(A

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velocity

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(B) In the given equation $F = P \cos(Ax) + Q \sin(Bt)$,the arguments of trigonometric functions must be dimensionless.Therefore,the dimensions of $(Ax)$ must be $[M^0 L^0 T^0]$.Since $[x] = [L]$,we have $[A][L] = [M^0 L^0 T^0]$,which implies $[A] = [L^{-1}]$.Similarly,the dimensions of $(Bt)$ must be $[M^0 L^0 T^0]$.Since $[t] = [T]$,we have $[B][T] = [M^0 L^0 T^0]$,which implies $[B] = [T^{-1}]$.Now,calculating the dimensions of the ratio $\left[\frac{B}{A}\right]$:$\left[\frac{B}{A}\right] = \frac{[T^{-1}]}{[L^{-1}]} = [L T^{-1}]$.The dimension $[L T^{-1}]$ corresponds to the physical quantity of velocity.

Force $F = P \cos(Ax) + Q \sin(Bt)$,where $x$ and $t$ are displacement and time respectively. Which one of the following physical quantities has the dimensions of $\left[\frac{B}{A}\right]$?

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