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  • This question has Statement I and Statment II. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement - I : A po

This question has Statement I and Statment II. Of the four choices given after the Statements, choose the one that best describes the two Statements.

Statement - I : A point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as f\left ( \frac{1}{2}mv^{2} \right )\; then\; f-\left ( \frac{m}{M+m} \right ).

Statement - II : Maximum energy loss occurs when the particles get stuck together as a result of the collision.

 

 

Option: 1

Statement - I is false,Statement - II is true.

 

 


Option: 2

Statement - I is true,Statement - II is true,Statement - II is a correct explanation of Statement - I.

 

 


Option: 3

Statement - I is true,Statement - II is true,Statement - II is not a correct explanation of Statement - I.

 

 


Option: 4

Statement - I is true,Statement - II is false.

 

 


Answers (1)

best_answer

Correct option (1) Statement I is false, Statement II is true

Explanation: Energy E =  E=\frac{p^2}{2m} where p is momentum, m is the mass moving of the particle

Maximum energy loss occurs when the particles get stuck together as a result of the collision.

\\ Maximum\ energy\ loss (\Delta E)=\frac{p^{2}}{2 m}-\frac{p^{2}}{2(m+M)}\\ where, $(m+M)$ \ is \ the \ resultant\ mass\ when\ the \ particles\ get\ stuck\\ . $$ \Delta E=\frac{p^{2}}{2 m}\left[1-\frac{m}{m+M}\right]=\frac{p^{2}}{2 m}\left[\frac{M}{m+M}\right] $$

\\ Also, \quad p=m v\\ \therefore \quad \Delta E=\frac{m^{2} v^{2}}{2 m}\left[\frac{M}{m+M}\right]=\frac{m v^{2}}{2}\left[\frac{M}{m+M}\right]\\ Comparing \ the\ expression\ with\ $$ \Delta E=f\left(\frac{1}{2} m v^{2}\right), f=\frac{M}{m+M} $$

Posted by

Sanket Gandhi

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