Fundamentals of Physics Chapter 9 Solutions: Center of Mass and Linear Momentum
Halliday Resnick & Walker Fundamentals of Physics Volume 1 Solutions for Chapter 9 ‘Center of Mass and Linear Momentum’ are the best study material for Class 12 and JEE. These Resnick Halliday Walker Solutions discuss various concepts including the centre of mass, linear momentum & its conservation, impulse, the system of a rocket, kinetic energy, Newton’s second law for a system of the particle, the elastic collision in one dimension, collision in two dimensions, etc. All these concepts are important for your competitive exams like IIT JEE Mains, JEE Advanced and NEET.
Physics Solutions for Resnick Halliday and Walker Volume 1 Center of Mass and Linear Momentum contain 128 questions that have been divided into 10 modules. All the modules cover different concepts of the chapter. Studying these questions will increase your overall understanding of the concepts and thus this exercise will help you to score well in your competitive exams.
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Important Topics for Resnick Halliday and Walker Fundamentals of Physics Volume 1 Solutions Chapter 9: Center of Mass and Linear Momentum
Center of mass: It is the point at which an object with a mass can be balanced. In other words, it is a point where the relative position of the distributed mass sums to zero.
Linear Momentum: You can find the momentum of an object by multiplying its mass with the velocity. The momentum of an object is defined by ‘p’. It is a vector quantity which means it possesses direction
Newton’s second law in terms of this momentum is given by, Fnet = dp/dt Here, F is force, p is momentum and dt is time derivative
Impulse: It is the force exerted on the body in a collision. It is denoted by J. You can calculate impulse by multiplying the net force on the object with the time period
Collision: It is an event where two or more bodies exert forces on each other in a short time period.
Conservation of Linear Momentum: In an isolated system where no external force is present, the linear momentum of the system remains constant i.e. p = constant
And according to the law of conservation of linear momentum, pi=pf where i is the initial time and f is the final time.
Inelastic collision: During a collision, if two bodies stick together, then it is called a completely inelastic collision.
Elastic Collisions in One Dimension: In this, the kinetic energy of two colliding bodies is conserved. When the system is isolated, its linear momentum is also conserved. In this collision, body 2 is the target, and body 1 is an incoming projectile. The conservation of kinetic energy and linear momentum produces the following expression for the velocities immediately after the collision:
For body 1: v1f = m1-m2/m1+m2 x v1i
For body 2: v2f = 2m1/ m1+m2 x v1i
Here, f is the final velocity and i is the initial velocity and m is the mass
Collisions in Two Dimensions: When two bodies collide and their motion is not along a single axis, then the collision is called a two-dimensional collision.
When the system is closed and isolated, the law of conservation of momentum applies to the collision which is written as:
p1i + p2i = p1f + p2f
Here, i is the initial value and f is the final value
Exercise Discussion of Halliday Resnick & Walker Fundamentals of Physics Volume 1 Solutions Chapter 9: Center of Mass and Linear Momentum
Module 1: Center of Mass
This module comprises 8 questions that are based on the topic of the centre of mass. The questions ask you to find coordinates of the centre of mass of different objects.
Module 2: Newton’s Second Law for a System of Particles
In this module of Resnick Halliday, you will find 8 questions that cover topics like displacement, friction, acceleration, velocity, the angle between the coordinates, unit vector notation, motion, and Newton’s second law of motion.
Module 3: Linear Momentum
This Resnick Halliday & Walker Fundamentals of Physics module contains 5 questions in total that will assess your understanding of linear momentum. The questions in this module ask you to find the magnitude of the momentum, the direction of momentum, change in linear momentum in unit vector notation, etc.
Module 4: Collision and Impulse
You will come across 16 questions in this module. These questions require your knowledge about different topics including force, momentum, linear momentum, collision, impulse, average force, velocity, change in momentum, the direction of impulse, force during the collision, etc.
Module 5: Conservation of linear momentum
This Resnick Halliday & Walker Physics module covers 10 questions that will test your knowledge of momentum and its conservation. You also have to use other concepts in these questions such as kinetic energy, spring force, velocity, the direction of velocity, speed, the energy released in a collision, gravitational force, unit vector notation, friction, the mass of an object, etc.
Module 6: Momentum and Kinetic Energy in Collisions
This module has 11 questions that possess a variety of situations to find the maximum compression in the spring, distance covered when the spring is compressed, speed of the spring gun, initial kinetic energy stored in the spring, speed of an object before and after the collision, total kinetic energy after the collision, loss of kinetic energy during a collision.
Module 7: Elastic Collisions in One Dimension
There are 11 questions in this module that will assess your understanding of elastic collisions in 1 dimension. You will come across different situations that ask you to calculate mass, height, distance, the center of mass, speed during a collision in one dimension.
Module 8: Collisions in Two Dimensions
This module contains 5 questions that ask you to find the initial & final speed of a particle during a collision, the angle between initial velocities, change in kinetic energy, the mass of a particle, etc.
Module 9: Systems with Varying Mass: A Rocket
This module of Resnick Halliday has 4 questions based on the topic of a rocket. You are asked about finding mass, speed, thurst, exhaust speed, velocity, and force of a rocket.
Module 10: Additional questions
This module has a total of 48 questions that cover all the concepts covered in the chapter such as collisions in one & two dimensions, the system of a rocket, momentum, kinetic energy, collision, impulse, the centre of mass, linear momentum, newton’s second law for a system of particles, etc.
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