A body of mass m1 moving at a constant speed undergoes an elastic collisio

Question

A body of mass m₁ moving at a constant speed undergoes an elastic collision with a body of mass

m_{2}

initially at rest. The ratio of the kinetic energy of mass

m_{1}

after the collision to that before the collision is

Options:

A . (m1−m2m1+m2)2

B . (m1+m2m1−m2)2

C . (2m1m1+m2)2

D . (2m2m1+m2)2

Answer: Option A
:
A
Let

u_{1}

be the speed of mass

m_{1}

before the collision.
Here

u_{2} = 0

. Therefore, the speeds of masses

m_{1}

and

m_{2}

after the collision respectively are

v_{1} = (\frac{m_{1} - m_{2}}{m_{1} + m_{2}}) u_{1}

and

v_{2} = (\frac{2 m_{1}}{m_{1} + m_{2}}) u_{1}

∴

KE of

m_{1}

after collision =

\frac{1}{2} m_{1} v_{1}^{2} = \frac{1}{2} m_{1} {(\frac{m_{1} - m_{2}}{m_{1} + m_{2}})}^{2} u_{1}^{2}

. KE of

m_{1}

before collision =

\frac{1}{2} m_{1} u_{1}^{2}

.
The ratio of the two is

{(\frac{m_{1} - m_{2}}{m_{1} + m_{2}})}^{2}

. Hence the correct choice is (a)

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. A completely inelastic collision is one in which the two colliding particles....

Question 2. A spacecraft of mass 'M' explodes into two parts when its velocity is 'V'. After the explosion, one&....left stationary. What is the velocity of the other part?

Question 3. A body of mass 'm' moving with a constant velocity 'v' hits another body of the same mass moving wit....it. The velocity of the compound body after collision is

Question 4. A ball of mass 'm' moving horizontally at a speed 'v' collides with the bob of a simple pendulum at ....immediately after the collision to that before the collision will be

Question 5. A body of mass 2 kg moving with a velocity (^i+2^j−3^k) ms−1 collides with another body of mass 3 kg ....together, the velocity in ms−1 of the composite body is

Question 6. A neutron of mass 1.67×10−27kg is moving with a velocity 1.2×107ms−1 collides head-on with a ....is perfectly inelastic, the speed of the composite particle will be

Question 7. A lead ball strikes a wall and falls down, a tennis ball having the same mass and velocity strikes the wall and bounces ....strikes the wall and bounces back. Check the correct statement

Question 8. A heavy steel ball of mass greater than 1 kg moving with a speed of 2 m sec−1collides head on with a station....After the collision the ping-pong ball moves approximately with speed

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0

Submit Solution

More Questions on This Topic :

Latest Videos

Latest Test Papers