The position of a particle moving on the x-ax | vedclass

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(C) The principle of homogeneity of dimensions states that only quantities with the same dimensions can be added or subtracted. Since $x(t)$ represent

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$L^2 T^{-2}$

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(C) The principle of homogeneity of dimensions states that only quantities with the same dimensions can be added or subtracted. Since $x(t)$ represents position,its dimension is $[L]$.$1$. For the term $A \sin t$: The argument of a trigonometric function must be dimensionless. Thus,$[A] = [x] = [L]$.$2$. For the term $B \cos^2 t$: Similarly,$[B] = [x] = [L]$.$3$. For the term $Ct^2$: Since $[Ct^2] = [x] = [L]$,we have $[C] [T^2] = [L]$,which implies $[C] = [L T^{-2}]$.$4$. For the term $D$: Since $D$ is added to $x(t)$,$[D] = [x] = [L]$.Now,calculate the dimension of $\frac{ABC}{D}$:$\left[ \frac{ABC}{D} ight] = \frac{[L] 	imes [L] 	imes [L T^{-2}]}{[L]} = [L^2 T^{-2}]$.

The position of a particle moving on the $x-$axis is given by $x(t) = A \sin t + B \cos^2 t + Ct^2 + D$,where $t$ is time. The dimension of $\frac{ABC}{D}$ is $-$

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