Force F is given in terms of time t and dista | vedclass

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(A) According to the principle of homogeneity of dimensions,the dimensions of each term added or subtracted in an equation must be the same.Given the

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$[M^0L^0T^0]$

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(A) According to the principle of homogeneity of dimensions,the dimensions of each term added or subtracted in an equation must be the same.Given the equation $F = a \sin(ct) + b \cos(dx)$,the dimensions of the terms $a \sin(ct)$ and $b \cos(dx)$ must be equal to the dimensions of force $F$.Since the arguments of trigonometric functions ($sin$ and $cos$) are dimensionless,the dimensions of $a$ and $b$ must be equal to the dimensions of force $F$.Dimension of force $F = [M^1L^1T^{-2}]$.Therefore,$[a] = [M^1L^1T^{-2}]$ and $[b] = [M^1L^1T^{-2}]$.Now,the dimension of $a/b$ is $[a]/[b] = [M^1L^1T^{-2}] / [M^1L^1T^{-2}] = [M^0L^0T^0]$.

Force $F$ is given in terms of time $t$ and distance $x$ by $F = a \sin(ct) + b \cos(dx)$. Then the dimension of $a/b$ is:

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