JEE Main 2025 Jan 29 Shift 1, Physics Q6: Units And Dimensions

JEE Main2025Jan 29, Shift 1Physics

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

$v = A t^{2} + \frac{B t}{C + t} .$

The dimension of $A B C$ is :

Solution

All terms on the RHS must have the dimension of velocity, $[L T^{- 1}] .$ Also, $C + t$ requires $C$ to have the dimension of time, $[C] = [T] .$

From $A t^{2} \sim [L T^{- 1}]$ : $[A] = [L T^{- 3}] .$

From $\frac{B t}{C + t} \sim [L T^{- 1}]$ : the ratio $t / (C + t)$ is dimensionless, so $[B] = [L T^{- 1}] .$

Multiplying: $[A B C] = [L T^{- 3}] \cdot [L T^{- 1}] \cdot [T] = [L^{2} T^{- 3}] = [M^{0} L^{2} T^{- 3}] .$

Concept behind this question

Concept-wise practice with instant solutions on Fundamenthol.