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

[JEE Main 2025, 23 Jan (Shift 1)]

Question

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

[JEE Main 2025, 23 Jan (Shift 1)]

YESPYQ · Accepted Answer

Correct answer: c) ${\mathrm{L}}^{2}{\mathrm{T}}^{-2}$. $x(t)=A\sin (t)+{Bcos}^{2}(t)+C{t}^{2}+D$ Here, A, B, C, and D are constants, and t is time. $[A]=L,[B]=L,[C]=\frac{L}{{T}^{2}},[D]=L\ \left[\frac{ABC}{D}\right]=\left[\frac{L\times L\times L{T}^{-2}}{L}\right]=\left[{L}^{2}{T}^{-2}\right]$

The position of a particle moving on x -axis is given by \(\mathrm{x}(\mathrm{t})=\mathrm{Asint}+{\mathrm{Bcos}}^{2}\mat…

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