Which of the following has the same dimension as that of linear momentum?

Impulse

The correct answer is option 3. Impulse.

The quantity that has the same dimension as that of linear momentum is Impulse.

Impulse is defined as the change in momentum of an object when a force is applied to it for a certain amount of time. Mathematically, impulse (J) is equal to the force (F) applied to an object multiplied by the time (Δt) over which the force is applied:

\[ J = F \cdot \Delta t \]

The dimensions of impulse are the same as those of momentum, which are mass times velocity \([MLT^{-1}]\). Therefore, impulse and linear momentum have the same dimensions.

While work and energy are related quantities, their dimensions are different from that of linear momentum. Work has dimensions of force times distance \([ML^2T^{-2}]\), and energy has dimensions of force times distance \([ML^2T^{-2}]\) as well.

Stress is a measure of force per unit area and has dimensions of force per unit area \([ML^{-1}T^{-2}]\), which are different from those of linear momentum.