Units & Dimensions

JEE Main level, single correct, medium

45 of 149

Question 45 of 149

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 :

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Answer: (D) \(\left[\mathrm{M}^0 \mathrm{~L}^2 \mathrm{~T}^{-3}\right]\)

[LT−1]=[A][T2]=[B][T][C]+[T][C]=[T][A]=[LT−3][B]=[LT−1][ABC]=[L2 T−3]\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}

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