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Dimensional Formula: The Dimensional Formula of any bodily amount is defined as the expression that represents how and which of the bottom portions are protected in that amount. It is denoted by enclosing the symbols for base portions with suitable strength in rectangular brackets i.e [ ].
An example is the Dimension Formula of Mass which is given as (M).
Momentum is the quality of a moving body that gives a certain impetus to the body. According to Newton’s second law, the rate of change of momentum of a body is called force. Thus, it is safe to say that momentum and its change are responsible for force.
The dimensional formula of Momentum is given as : M¹L¹T-1
Where M refers to Mass
L refers to Length
and T refers to Time
With all units in their standard form.
Derivation of Dimensional formula of Momentum :
The formula for momentum is given as :
P = M×V
Where “M” is the mass of the object and “V” is the velocity of the same object.
Since the dimensional unit of Mass is [M] and velocity is given as distance per unit time, its dimensional formula would be the ratio of length and time i.e [LT-1]
Combining the dimensional formulae of Mass and velocity to make the dimensional formula of momentum, we get : [P] = M×LT-1
Thus, [P] = MLT-1
The dimensional formula of momentum is not only important for theoretical purposes but also for checking the formula of different quantities.
Momentum
When two or more bodies are acting upon each other, the complete momentum is said to be constant unless an external force is applied. This is known as the law of conservation of linear momentum.
Thus, momentum can neither be created nor destroyed. In other words, between two objects, the total momentum that takes place before the collision is equal to the total momentum after the collision. The total momentum tends to be conserved – it is constant or doesn’t change.
Further, we will understand about the law of conservation of linear momentum and its applications.
Logic behind the law of conservation of momentum:
Let us assume that a collision is happening between two objects, object A and object B. In such a collision, the forces which are acting between the objects have equal magnitude but are acting opposite in direction, which is Newton’s third law. It can be denoted as
F1 = -F2
These forces act for a certain period of time, sometimes the time can be long and sometimes it can be short. Irrespective of how long or short the time is, it is said that the time which is acting upon object 1 is equal to the time acting upon object 2. This is completely logical. This is given by t1 = t2.
With the above statements, it is clear that the forces acting are equal in magnitude and opposite in direction and the times on which they are acting are equal in magnitude, it means that the impulses which are experienced by two objects are also equal in magnitude and opposite in direction. It can be expressed in the equation form,
F1*t1 = F2*t2
But the impulse experienced by an object tends to be equal to the change in momentum of that object, this is the impulse momentum change theorem. Logically if each object experiences equal and opposite impulse, it will also experience equal and opposite momentum
m1*Δv1 = -m2*Δv2
Let us understand the law of conservation of momentum using a real life analogy, this involves money transactions between two people, say there are two friends John and Seema. John has $100 and even Seema has $100, the total amount of money before any transaction taking place is $200. John gives 50$ to Seema and now Seema has 150$ and John has 50$ but the total amount even after the transaction is 200$, which means the money before and after transaction remains constant.
Conclusion
The dimensional formula of momentum can be calculated by applying the basic formula of product of mass and velocity, and putting their dimensions in the formula. Dimensional analysis has numerous practical applications and it can also be used for checking formulas of different quantities.
