Let force F = Asin (Ct) + Bcos (Dx), where x and t are displacement and time, respectively. The dimensions of C/D are same as dimensions of (a) angular velocity (b) velocity (c) angular momentum (d) velocity gradient

Answer: (b). The argument of sine or cosine must be dimensionless. Ct dimensionless ⇒ [C] = [T⁻¹]; Dx dimensionless ⇒ [D] = [L⁻¹]. [C/D] = [LT⁻¹], which is velocity. So the answer is (b) velocity.

Let force F = Asin (Ct) + Bcos (Dx), where x and t are displacement… | MHT CET 2020 (16 Oct, Shift 1)

Q50MHT CET 2020 · 16 OCT · SHIFT 1Easy

Applications of Dimensional Analysis

Let force $F = A\sin(Ct) + B\cos(Dx)$ , where $x$ and $t$ are displacement and time, respectively. The dimensions of $\frac{C}{D}$ are same as dimensions of

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Answer: (b)

The argument of sine or cosine must be dimensionless.
$Ct$ dimensionless $\Rightarrow [C] = [T^{-1}]$ ; $Dx$ dimensionless $\Rightarrow [D] = [L^{-1}]$ .
$[C/D] = [LT^{-1}]$ , which is velocity.
So the answer is (b) velocity.

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