The expression given below shows the variation of velocity \((v)\) with time (t),…

The expression given below shows the variation of velocity \((v)\) with time (t), \(v=\mathrm{At}^2+\frac{\mathrm{Bt}}{\mathrm{C}+\mathrm{t}}\). The dimension of ABC is :
  1. \(\left[\mathrm{M}^0 \mathrm{~L}^1 \mathrm{~T}^{-3}\right]\)
  2. \(\left[\mathrm{M}^0 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]\)
  3. \(\left[\mathrm{M}^0 \mathrm{~L}^1 \mathrm{~T}^{-2}\right]\)
  4. \(\left[\mathrm{M}^0 \mathrm{~L}^2 \mathrm{~T}^{-3}\right]\)

Solution

$\begin{aligned} & {\left[\mathrm{LT}^{-1}\right]=[\mathrm{A}]\left[\mathrm{T}^2\right]=\frac{[\mathrm{B}][\mathrm{T}]}{[\mathrm{C}]+[\mathrm{T}]}} \\ & {[\mathrm{C}]=[\mathrm{T}]} \\ & {[\mathrm{A}]=\left[\mathrm{LT}^{-3}\right]} \\ & {[\mathrm{B}]=\left[\mathrm{LT}^{-1}\right]} \\ & {[\mathrm{ABC}]=\left[\mathrm{L}^2 \mathrm{~T}^{-3}\right]}\end{aligned}$

Asked in: JEE Main 2025 (29 Jan Shift 1)

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