
Four smooth steel balls of equal mass at rest are free to move along a straight line without friction. The first ball is given a velocity of $0.4\,m{s^{ - 1}}$. It collides head on with the second elastically, the second one similarly with the third and so on. The velocity of the last ball is
A. $0.4\,m{s^{ - 1}}$
B. $0.2\,m{s^{ - 1}}$
C. $0.1\,m{s^{ - 1}}$
D. $0.05\,m{s^{ - 1}}$
Answer
162k+ views
Hint: In order to solve this question, we will use the concept of head on elastic collision in which when two bodies of same mass collide with each other the body which was at rest gets whole energy of moving body, so using this we will determine the velocity of the fourth and last ball.
Complete step by step solution:
Elastic collisions are those where total momentum of the system before the collision is always equal to the final momentum of the system after the collision and total kinetic energy of the system before the collision is equal to the final kinetic energy of the system after the collision and in between these bodies interchange the velocities with different magnitudes.
But in head on elastic collision between two bodies of equal mass and if one of the bodies was at rest before the collision then after the collision the moving body comes to rest and the body which was at rest initially starts moving with the same velocity with which another body was moving.
Here, we have given four balls of equal mass and all was at rest initially and first body starts moving with velocity of $0.4\,m{s^{ - 1}}$ and when it hits second body as head-on collision second body will acquired the velocity of $0.4\,m{s^{ - 1}}$ from first body and later third body will acquired the velocity of $0.4\,m{s^{ - 1}}$ from second body and at last fourth body will acquired the velocity of $0.4\,m{s^{ - 1}}$ from third body. So the final velocity of the last and fourth ball is $0.4\,m{s^{ - 1}}$.
Hence, the correct answer is option A.
Note: It should be remembered that, when the last ball will acquire the velocity it will simply continue to move with same velocity if there are no resistive forces and if bodies were of different mass then all bodies acquire different velocities depending upon the mass.
Complete step by step solution:
Elastic collisions are those where total momentum of the system before the collision is always equal to the final momentum of the system after the collision and total kinetic energy of the system before the collision is equal to the final kinetic energy of the system after the collision and in between these bodies interchange the velocities with different magnitudes.
But in head on elastic collision between two bodies of equal mass and if one of the bodies was at rest before the collision then after the collision the moving body comes to rest and the body which was at rest initially starts moving with the same velocity with which another body was moving.
Here, we have given four balls of equal mass and all was at rest initially and first body starts moving with velocity of $0.4\,m{s^{ - 1}}$ and when it hits second body as head-on collision second body will acquired the velocity of $0.4\,m{s^{ - 1}}$ from first body and later third body will acquired the velocity of $0.4\,m{s^{ - 1}}$ from second body and at last fourth body will acquired the velocity of $0.4\,m{s^{ - 1}}$ from third body. So the final velocity of the last and fourth ball is $0.4\,m{s^{ - 1}}$.
Hence, the correct answer is option A.
Note: It should be remembered that, when the last ball will acquire the velocity it will simply continue to move with same velocity if there are no resistive forces and if bodies were of different mass then all bodies acquire different velocities depending upon the mass.
Recently Updated Pages
A steel rail of length 5m and area of cross section class 11 physics JEE_Main

At which height is gravity zero class 11 physics JEE_Main

A nucleus of mass m + Delta m is at rest and decays class 11 physics JEE_MAIN

A wave is travelling along a string At an instant the class 11 physics JEE_Main

The length of a conductor is halved its conductivity class 11 physics JEE_Main

Two billiard balls of the same size and mass are in class 11 physics JEE_Main

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Displacement-Time Graph and Velocity-Time Graph for JEE

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Class 11 JEE Main Physics Mock Test 2025

JoSAA JEE Main & Advanced 2025 Counselling: Registration Dates, Documents, Fees, Seat Allotment & Cut‑offs

Other Pages
NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

Motion in a Straight Line Class 11 Notes: CBSE Physics Chapter 2

NCERT Solutions for Class 11 Physics Chapter 2 Motion In A Straight Line

Important Questions for CBSE Class 11 Physics Chapter 1 - Units and Measurement
