Question

show that the dimension of momentum per unit area per unit time are the same as those of force per unit area

Answer 1

Answer:

Unit of,

momentum = kg×m/s

momentum per unit area = kg×m/s×m² = kg/m×s

momentum per unit area per unit time= kg/ms²

force = kg×m/s²

force per unit area = kg×m/s²×m² = kg/ms²

Explanation:

Answer 2

Given:

The dimension of momentum = [M¹L¹T⁻¹]

The dimensions of force = [M¹L¹T⁻²]

To Proof:

The dimensions of momentum per unit area per unit time are equal to that of force per unit area.

Solution:

Momentum is the dot product of the mass and velocity of an object.

⇒ p = m× v

The unit of momentum is Netwon-second or kg-m/s.

The dimension of momentum = [M¹L¹T⁻¹]

Dividing the above expression with the dimension of area and time.

⇒ [M¹L¹T⁻¹]/ [M⁰L²T⁰][M⁰L⁰T¹] =  [M¹L⁻¹T⁻²]

Force is the magnitude of a push or pull. And is the dot product of the mass of a body and its acceleration.

⇒ F = m×a

The unit of force is Newton or kg-m/s².

The dimension of force = [M¹L¹T⁻²]

Dividing the above expression with the dimension of the area.

⇒  [M¹L¹T⁻²]/ [M⁰L²T⁰] = [M¹L⁻¹T⁻²]

Hence proved that the dimension of momentum per unit area per unit time is equal to the dimension of force per unit area.