# Dimension of Linear Momentum

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## What are Dimensions?

The powers to which the fundamental units that are the unrelated units of measurement are raised for a physical quantity so as to get one unit of that quantity is considered as dimensions of that physical quantity.

### Dimensional Formula

Dimensional formulas are often defined as the expression that shows the powers to which the fundamental units are to be raised to get one unit of a derived quantity.

Suppose the unit of a derived quantity is represented by Q. Then, Q can be given as- MaLbTc

Thus, Q= MaLbTc

Which represents the dimensional formula of a physical quantity and the exponents in this case (a,b,c) are the dimensions.

### Linear Momentum

From study of Momentum, we know that momentum is mass of the body times the velocity.

So mathematically p= m x v

Change in the momentum of the body remains proportional to the net force and the time over which the net force acts.

Now, we will find out how momentum and net force are related.

While learning kinematic equations, you have learned that with constant acceleration, the change in velocity Δv can also be given as aΔt.

So, the change in momentum following an acceleration can be given as-

Δp= mΔv

Therefore, m(aΔt)= FnetΔt

From the above equation, by rearranging the equation to get value of Fnet

Given the mass and the net force is constant

Fnet= Δp/Δt

From this, we can conclude that change in momentum is equal to the net force over a period of time.

Now, inertia of translational momentum is described as linear momentum. Linear momentum does not have a direction as it is a vector quantity. Also, it has to be noted that the body’s momentum is in the same direction as its vector of velocity.

The SI unit of linear momentum is given as Kg m/s

### Formula for Dimensions of Linear Momentum

Linear Momentum is given by -

Linear Momentum  = Mass∗Velocity

Dimensions of

Mass=[M]

Dimensions Of

Velocity=[Length] / [Time]= [LT to the power -1]

Therefore,

Dimensions of

Linear Momentum is given by-

[M1 L1 T-1]

Where,

• M = Mass

• L = Length

• T = Time

### Solved Examples to Calculate Linear Momentum

1. Find the linear momentum of the body having mass 10 kg, moving with the speed of 40 m/s.

Solution- Given mass of the body m= 10 kg

Velocity of the body v= 4 m/s

Linear momentum is given by-

P = mv

So, Momentum p= 10 x 40

p= 400 kg m/s

2. The linear momentum of a body of mass 5 kg is 40 kg m/s. What is the velocity with which the object is moving?

Solutions- Mass of the body is m= 5 kg

Given linear momentum of the body p = 40 kgm/s

Linear momentum is given as p= mv

Rearranging the equation, v = P / m

So, v = 40 / 5

v = 8 m/s

### Derivation of Dimension of Linear Momentum

Linear Momentum = Mass × [Velocity] . . . . . . (1)

The dimensional formula of,

Mass = [M1 L0 T0] . . . . (2)

Velocity = [M0 L1 T-1] . . . . (3)

Let us substitute equation (2) and (3) in equation (1). Hence, we get,

Linear Momentum = Mass × [Velocity]

Or, L = [M1 L0 T0] × [M0 L1 T-1] = [M1 L1 T-1].

Therefore, the dimensional formula for linear momentum can be given by [M1 L1 T-1].

Q1. What is Linear Momentum? Give its Dimensional Formula.

Answer- Linear Momentum is given by-

Linear Momentum  = Mass∗Velocity

Dimensions of

Mass=[M]

Dimensions Of

Velocity=[Length] / [Time]= [LT to the power -1]

Therefore,

Dimensions of

Linear Momentum is given by-

[M1 L1 T-1]

Where,

• M = Mass

• L = Length

• T = Time

Q2. Derive the Dimensions of Linear Momentum

Answer- Linear Momentum = Mass × [Velocity] . . . . . . (1)

The dimensional formula of,

Mass = [M1 L0 T0] . . . . (2)

Velocity = [M0 L1 T-1] . . . . (3)

Let us substitute equation (2) and (3) in equation (1). Hence, we get,

Linear Momentum = Mass × [Velocity]

Or, L = [M1 L0 T0] × [M0 L1 T-1] = [M1 L1 T-1].

Therefore, the dimensional formula for linear momentum can be given by [M1 L1 T-1].

Q3. Where can I learn the Dimensional Formula of Physical Quantities?

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