The dimensional formula for impulse is

The correct option is MLT⁻¹.

Step-by-step derivation:

Impulse is defined as the product of the average force acting on an object and the time interval for which the force is applied. The formula for impulse is:

$\text{Impulse}=\text{Force}\times \text{Time}$

To find the dimensional formula of impulse, we determine the dimensions of force and time:

1. Force: According to Newton's second law, force is mass multiplied by acceleration. The dimension of mass is [M] and the dimension of acceleration is [LT⁻²]. Thus, the dimensional formula for force is:

$\left[\text{Force}\right]=\left[{\text{MLT}}^{-2}\right]$

2. Time: The dimensional formula for time is:

$\left[\text{Time}\right]=\left[\text{T}\right]$

Now, we substitute these dimensions back into the impulse formula:

$\left[\text{Impulse}\right]=\left[{\text{MLT}}^{-2}\right]\times \left[\text{T}\right]$

Multiplying the exponents of time yields:

$\left[\text{Impulse}\right]=\left[{\text{MLT}}^{-1}\right]$

Therefore, the dimensional formula for impulse is MLT⁻¹.