Linear Dimensional Formula of Momentum Overview
Linear momentum is defined as the product of an object's mass and velocity. It is a vector value. It is denoted by the sign p. The direction of a body's momentum is the same as the direction of its velocity. Momentum is a conserved quantity, which means that in an isolated system, the overall momentum remains constant. Linear momentum is measured in kg/s (kilograms per second).
What are Dimensions?
The dimensions of a physical quantity are the powers to which the basic units, which are unrelated units of measurement, are increased in order to obtain one unit of that quantity.
What is Linear Momentum?
Linear momentum is a property of a moving body that provides it with impetus. The rate of change in the momentum of a body is known as its "force," according to Newton's second law. As a result, it is acceptable to state that linear momentum and its change are to blame for force.
What is the Formula for Linear Momentum?
The formula for the linear momentum of a body is given by-
Where,
m = mass of the object
v = velocity of the object
What is the Dimensional Formula?
Any quantity's dimensional formula is the phrase that shows the powers to which the basic units must be increased in order to get one unit of a derived quantity.
What is the Dimensional Formula of Momentum?
The momentum dimensional formula is provided by-
Where,
M = Mass
L = Length
T = Time
Read More About- Dimension of Momentum
Derivation for Dimensional Formula of Momentum
The below is the derivation of the dimensional formula of momentum-
Momentum (M) = Mass × Velocity (1)
The dimensional formula of velocity = (M⁰ L¹ T⁻¹) (2)
The dimensional formula of mass = (M¹ L⁰ T⁰) (3)
On substituting equation (2) and (3) in equation (1) we get,
M = [M1 L⁰ T⁰] × [M⁰ L¹ T⁻¹]
= [M1 L¹ T⁻¹]
Significance of Dimension of Momentum in IIT JEE Exam
Every aspect of a subject's chapter must be approached holistically. Not only will it fully prepare you for the test, but it will also clarify your grasp of each topic. It will assist you with IIT preparation and answering conceptual questions in the test. There would be one or two questions from the chapter unit and dimensions, with a weight of about four marks.
Read Recently Updated Exams - IIT JEE Main 2023 and IIT JEE Advanced 2023.
Points to Remember
- Linear momentum is a vector quantity determined by multiplying an object's mass by its velocity.
- Linear momentum is measured in kg/s.
- [M1L1T-1] is the dimensional formula for linear momentum.
- The direction of linear momentum is the same as the direction of the object's velocity.
- If the net external force exerted on a system is zero, its linear momentum remains constant. This implies that momentum is preserved.
Conclusion
By using the fundamental formula of the product of mass and velocity and then placing their dimensions in the formula, the dimensional formula of linear momentum can be computed. Linear momentum is a physics concept that establishes the product of a particle's mass and velocity. It assesses the force and considers the influence of each particle. Applying the concept of conservation of momentum is also significant since it aids in the prevention of collisions. It also examines the system of particles that are traveling faster.
Sample Questions for Dimensional Formula of Momentum
Sample Question 1- Determine the linear momentum of a body weighing 8 kg and traveling at a speed of 78 m/s.
m = 8 kg
v = 78 m/s
Linear momentum, p = m⋅v
p = 8 × 78
= 624 kg m/s
The linear momentum of this body is 624 kg m/s.
Sample Question 2- A child sits motionless at the end of a long trolley moving on a smooth horizontal path at a uniform speed. If the child runs about the trolley randomly, then what is the speed of the center of mass of the system?
When the youngster starts running around the trolley in any way, the speed of the system's center of mass remains constant. In this case, the child and the trolley function as a single system, with just internal forces acting. As a result, the system's momentum is conserved, and the velocity remains constant.
Sample Question 3- Explain linear momentum conservation.
The law of conservation of linear momentum states that if the net external force on a system is zero, then the linear momentum is conserved. The linear momentum of the individual particles in the system keeps changing, but the overall linear momentum of the system remains constant unless an external force acts on it.
Sample Question 4- Determine the mass of an object traveling at a velocity of 50 m/s if its linear momentum is 89 kg m/s.
v = 50 m/s
p = 89 kg m/s
The formula for linear momentum is p = m⋅v
89 = m × 50
m = 1.78 kg
So, the mass of this object is 1.78 kg.
Sample Question 5- A 28 kg item is at rest. Determine its linear momentum.
Here, the given object of mass 28 kg is at rest, which means its velocity is zero.
Now, we know linear momentum is calculated as p = m⋅v
p = 28 × 0 = 0
Thus, the linear momentum of the given object is zero.
Sample Question 6- Is the universe's overall momentum constant? Explain.
The universe's entire momentum remains constant. There is no system greater than the cosmos itself. As there is no outside force acting on the cosmos, its linear momentum is preserved.
Sample Question 7- If the linear momentum of a 9 kg object is 81 kg m/s, determine its velocity.
m = 9 kg
p = 81 kg m/s
Linear momentum, p = m⋅v
81 = 9 × v
v = 9 m/s
So, the velocity of this object is 9 m/s.