The dimensions of impulse are equal to that of

The correct option is linear momentum.

To find which quantity has the same dimensions as impulse, let us analyze the dimensional formulas for both impulse and linear momentum step-by-step.

1. Understanding Impulse:
Impulse ($I$) is defined as the product of force ($F$) and the time interval ($t$) over which it acts:
$I=F·t$

The dimensional formula for force ($F=\text{mass}\times \text{acceleration}$) is:
$\left[F\right]=\left[M{L}^1{T}^{-2}\right]$

The dimensional formula for time ($t$) is:
$\left[t\right]=\left[T\right]$

Therefore, the dimensional formula for impulse is:
$\left[I\right]=\left[ML{T}^{-2}\right]·\left[T\right]=\left[ML{T}^{-1}\right]$

2. Understanding Linear Momentum:
Linear momentum ($p$) is defined as the product of mass ($m$) and velocity ($v$):
$p=m·v$

The dimensional formula for mass ($m$) is:
$\left[m\right]=\left[M\right]$

The dimensional formula for velocity ($v$) is:
$\left[v\right]=\left[L{T}^{-1}\right]$

Therefore, the dimensional formula for linear momentum is:
$\left[p\right]=\left[M\right]·\left[L{T}^{-1}\right]=\left[ML{T}^{-1}\right]$

Conclusion:
Comparing the two dimensional formulas, we find that both impulse and linear momentum have the identical dimensions of:
$\left[ML{T}^{-1}\right]$

This is also in accordance with the Impulse-Momentum Theorem, which states that the impulse applied to an object is equal to the change in its linear momentum ($I=\Delta p$).