Question

A particle of mass $m_{1}$ is moving with a velocity $v_{1}$ and another particle of mass $m_{2}$ is moving with a velocity $v_{2} .$ Both have the same momentum, but their different kinetic energies are $E_{1}$ and $E_{2}$ respectively. If $m_{1}>m_{2}$ then: (a) $E_{1}=E_{2}$ (b) $E_{1}<E_{2}$ (c) $\frac{E_{1}}{E_{2}}=\frac{m_{1}}{m_{2}}$ (d) $E_{1}>E_{2}$

Name: Problem 34, Chapter 4: Objective Physics : NEET 2020 Examination textbook Gurukul Oswal
Uploaded: 2021-09-30T13:42:48-08:00
Duration: 1 min 55 s
Channel: Dheeraj Sharma
Description: A particle of mass m1 is moving with a velocity v1 and another particle of mass m2 is moving with a velocity v2 . Both have the same momentum, but their different kinetic energies are E1 and E2 respectively. If m1>m2 then: (a) E1=E2 (b) E1 E2

   A particle of mass $m_{1}$ is moving with a velocity $v_{1}$ and another particle of mass $m_{2}$ is moving with a velocity $v_{2} .$ Both have the same momentum, but their different kinetic energies are $E_{1}$ and $E_{2}$ respectively. If $m_{1}>m_{2}$ then:
(a) $E_{1}=E_{2}$
(b) $E_{1}<E_{2}$
(c) $\frac{E_{1}}{E_{2}}=\frac{m_{1}}{m_{2}}$
(d) $E_{1}>E_{2}$

Objective Physics : NEET 2020 Examination textbook Gurukul Oswal

Gurukul Oswal… 2020 Edition

Chapter 4, Problem 34

Instant Answer

Solved by Expert Dheeraj Sharma

09/30/2021

Step 1

Step 1: Given that the momentum of both particles is the same, we can write $m_{1}v_{1} = m_{2}v_{2} = P$, where $P$ is the momentum. Show more…

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A particle of mass $m_{1}$ is moving with a velocity $v_{1}$ and another particle of mass $m_{2}$ is moving with a velocity $v_{2} .$ Both have the same momentum, but their different kinetic energies are $E_{1}$ and $E_{2}$ respectively. If $m_{1}>m_{2}$ then: (a) $E_{1}=E_{2}$ (b) $E_{1}<E_{2}$ (c) $\frac{E_{1}}{E_{2}}=\frac{m_{1}}{m_{2}}$ (d) $E_{1}>E_{2}$

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Key Concepts

Momentum

Momentum is a fundamental concept in mechanics defined as the product of an object's mass and its velocity. It is a conserved quantity in isolated systems and serves as the basis for analyzing collisions and interactions between moving objects. Understanding momentum allows one to relate the motion of different objects, even when their masses and velocities vary, provided specific conditions such as equal momentum are met.

Kinetic Energy

Kinetic energy is the energy that an object possesses due to its motion, traditionally defined as one half the product of its mass and the square of its velocity. It is a scalar quantity that reflects how mass and velocity contribute to the energy of motion. In the context of fixed momentum, kinetic energy is inversely proportional to the mass of a particle, meaning that for a constant momentum, an object with a smaller mass will have a higher kinetic energy.

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