The expression given below shows the variation of velocity (v) with time (t), v = At² + Bt/C+t. The dimension of ABC is: (a) [M0L1T−2] (b) [M0L2T−3] (c) [M0L2T−2] (d) [M0L1T−3]

Answer: (b). [At²] = [LT⁻¹] ⇒ [A] = [LT⁻³]. C is added to t: [C] = [T]; then Bt/(C+t) has dimensions of B, so [B] = [LT⁻¹]. [ABC] = [LT⁻³][LT⁻¹][T] = [M⁰L²T⁻³]. So the answer is (b).

The expression given below shows the variation of velocity (v) with… | JEE Main 2025 (29 Jan, Shift 1)

Q13JEE Main 2025 · 29 JAN · SHIFT 1Easy

Applications of Dimensional Analysis

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

$v = \mathrm{At^{2}} + \frac{\mathrm{Bt}}{\mathrm{C+t}}$ .

The dimension of ABC is:

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Answer: (b)

$[At^2] = [LT^{-1}] \Rightarrow [A] = [LT^{-3}]$ .
$C$ is added to $t$ : $[C] = [T]$ ; then $Bt/(C+t)$ has dimensions of $B$ , so $[B] = [LT^{-1}]$ .
$[ABC] = [LT^{-3}][LT^{-1}][T] = [M^0L^2T^{-3}]$ .
So the answer is (b).

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