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Linear Momentum

Force And The Laws Of Motion - Concepts

Newtons Law of Motion

Linear Momentum

Conservation of Linear Momentum

Sports and Second Law of Motion

Class - Railways Subjects

Concept Explanation

Linear Momentum

Momentum measures the quantity of motion possessed by a body. It is defined as the product of the mass of a body and its velocity. For a linear motion it is called the linear momentum of the body. It is the vector quantity which means that the body's momentum is always in the same direction as its velocity vector. It is a conserved quantity which means that the total momentum of the system is constant. If “m” is the mass and “v” be the velocity of a body at some instant, the linear momentum is given by the expression -

$p:=:mtimes:v$

Here, p = momentum, v = velocity and m = mass

As momentum and velocity are the vector quantities therefore, they are denoted as $underset{p}{rightarrow}$ and $underset{v}{rightarrow}$ respectively.

The SI unit of momentum is kg m/s

Examples:

1. A bullet fired at a wooden board can destroy it. But a small stone of the same mass as the bullet when thrown at the board will hardly cause any damage.Although their masses are the same, the high velocity of the bullet gives it a larger momentum, which causes the damage.

2.Consider, a truck and a rickshaw moving with the same velocities, heading towards each other and eventually ending up in a head on collision. The rickshaw could might get deformed to such an extend that it would be difficult for us to make it, while truck might get some minor damages.This is because of the larger momentum of the truck.

Illustration: A ball with a 500g mass is thrown with a velocity of 72 km/h. What is the initial momentum?

Solution: Given

mass of the ball = 500g = 0.5 Kg and

velocity of the ball = 72 km/h = 20 m/s

Momentum of the ball

$p:=:mv:=:frac{1}{2}:times20:=:10:kg:m/s$

Illustration: The linear momentum of a body is 40 kg m/s and the mass of the object is 5 kg. Determine the velocity of the object.

Solution: Given parameters are,

m = 5 kg and

p = 40 kg m/s

Linear momentum formula is given by

$p:=:mv$

$v;=:frac{p}{m}$ $Rightarrow frac{40}{5}Rightarrow 8:m/s$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

A Body of mass 10Kg collides against a wall with velocity 5m/s and rebounds with the same speed. the change in momentum is
A. 0 Kg m/s	B. -100 g m/s	C. -100 Kg m/s	D. 100 Kgm/s
Right Option : C
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Question : 2

A body, whose momentum is constant, must have constant-
A. Force	B. Velocity	C. Acceleration	D. All of these
Right Option : B
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Question : 3

Which of the following are correct ? (a) Momentum measures the quantity of motion possessed by a body. (b) It is defined as the product of the mass of a body and its velocity for a linear motion it is called the linear momentum of the body. (c) The SI unit of momentum is kg m/s .
A. Only (a) and (b) is correct .		B. Only (b) and (c) is correct .
C. Only (a) and (c) is correct .		D. All of these .
Right Option : D
View Explanation