JEE MAIN - Physics (2025 - 29th January Morning Shift - No. 5)
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 :
[M0L1T−2]
[M0L2T−3]
[M0L2T−2]
[M0L1T−3]
Explanation
$$\begin{aligned}
& {\left[\mathrm{LT}^{-1}\right]=[\mathrm{A}]\left[\mathrm{T}^2\right]=\frac{[\mathrm{B}][\mathrm{T}]}{[\mathrm{C}]+[\mathrm{T}]}} \\
& {[\mathrm{C}]=[\mathrm{T}]} \\
& {[\mathrm{A}]=\left[\mathrm{LT}^{-3}\right]} \\
& {[\mathrm{B}]=\left[\mathrm{LT}^{-1}\right]} \\
& {[\mathrm{ABC}]=\left[\mathrm{L}^2 \mathrm{~T}^{-3}\right]}
\end{aligned}$$
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