The position of a particle moving on x -axis is given by x(t) = Asin t + Bcos ² t + Ct² + D, where t is time. The dimension of ABC/D is (a) L (b) L³T⁻² (c) L²T⁻² (d) L²

Answer: (c). sin t and cos ² t are dimensionless, so [A] = [B] = [D] = [L]. [Ct²] = [L] ⇒ [C] = [LT⁻²]. [ABC/D] = [L][L][LT⁻²]/[L] = [L²T⁻²]. So the answer is (c).

The position of a particle moving on x -axis is given by x(t) = Asin… | JEE Main 2025 (23 Jan, Shift 1)

Q14JEE Main 2025 · 23 JAN · SHIFT 1Easy

Applications of Dimensional Analysis

The position of a particle moving on $x$ -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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Answer: (c)

$\sin t$ and $\cos^2 t$ are dimensionless, so $[A] = [B] = [D] = [L]$ .
$[Ct^2] = [L] \Rightarrow [C] = [LT^{-2}]$ .
$[ABC/D] = [L][L][LT^{-2}]/[L] = [L^2T^{-2}]$ .
So the answer is (c).

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