Explanation:

To determine which pair does not have identical dimensions, we need to understand the dimensions of each physical quantity involved.

Angular Momentum:
Angular momentum is the product of moment of inertia and angular velocity. The dimensions of angular momentum are given by [M L^2 T^-1], where M represents mass, L represents length, and T represents time.

Planck's Constant:
Planck's constant is a fundamental constant in quantum mechanics. Its dimensions are given by [M L^2 T^-1], which is the same as the dimensions of angular momentum.

Moment of Inertia:
Moment of inertia is a measure of an object's resistance to changes in its rotational motion. Its dimensions are given by [M L^2], where M represents mass and L represents length.

Moment of a Force:
The moment of a force, also known as torque, is a measure of the force's tendency to cause rotational motion. Its dimensions are given by [M L^2 T^-2], where M represents mass, L represents length, and T represents time.

Work:
Work is the product of force and displacement. Its dimensions are given by [M L^2 T^-2], which is the same as the dimensions of torque.

Torque:
Torque is another name for moment of a force, and its dimensions have already been mentioned above.

Impulse:
Impulse is the product of force and time. Its dimensions are given by [M L T^-1], where M represents mass, L represents length, and T represents time.

Momentum:
Momentum is the product of mass and velocity. Its dimensions are given by [M L T^-1], which is the same as the dimensions of impulse.

Comparison:
Now, let's compare the dimensions of each pair:

- Angular momentum and Planck's constant have identical dimensions of [M L^2 T^-1].
- Work and torque also have identical dimensions of [M L^2 T^-2].
- Impulse and momentum have identical dimensions of [M L T^-1].

The only pair that does not have identical dimensions is moment of inertia and moment of a force. Moment of inertia has dimensions of [M L^2], while moment of a force has dimensions of [M L^2 T^-2]. Therefore, the correct answer is option B.

Moment of inertia and moment of a force