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System of Particles and Rotational Motion

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12

This question has Statement I and Statement 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 open parentheses 1 half mv squared close parentheses comma space then space straight f space equals space open parentheses fraction numerator straight m over denominator straight M plus straight m end fraction close parentheses
Statement – II : Maximum energy loss occurs when the particles get stuck together as a result of the collision.

  • Statement – I is true, Statement – II is true, Statement – II is a correct explanation of Statement – I.

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

  • Statement – I is true, Statement – II is false.

  • Statement – I is false, Statement – II is true 


D.

Statement – I is false, Statement – II is true 

Before collision, the mass is m and after collision, the mass is m+M
therefore, Maximum energy loss
fraction numerator straight p squared over denominator 2 straight m end fraction minus fraction numerator straight p squared over denominator 2 left parenthesis straight m plus straight M right parenthesis end fraction
space equals space fraction numerator straight p squared over denominator 2 straight m end fraction open square brackets fraction numerator begin display style straight m end style over denominator straight m plus straight M end fraction close square brackets space space space space
space space space open square brackets because KE space equals space fraction numerator straight p squared over denominator 2 straight m end fraction close square brackets
equals space 1 half mv squared open curly brackets fraction numerator straight m over denominator straight m plus straight M end fraction close curly brackets
open square brackets straight f space equals space fraction numerator straight m over denominator straight m plus straight M end fraction close square brackets

Before collision, the mass is m and after collision, the mass is m+M
therefore, Maximum energy loss
fraction numerator straight p squared over denominator 2 straight m end fraction minus fraction numerator straight p squared over denominator 2 left parenthesis straight m plus straight M right parenthesis end fraction
space equals space fraction numerator straight p squared over denominator 2 straight m end fraction open square brackets fraction numerator begin display style straight m end style over denominator straight m plus straight M end fraction close square brackets space space space space
space space space open square brackets because KE space equals space fraction numerator straight p squared over denominator 2 straight m end fraction close square brackets
equals space 1 half mv squared open curly brackets fraction numerator straight m over denominator straight m plus straight M end fraction close curly brackets
open square brackets straight f space equals space fraction numerator straight m over denominator straight m plus straight M end fraction close square brackets

398 Views

Is it necessary that there should be matter at the centre of mass of system?

No, it is not necessary that there be matter at the centre of mass of the system.

For e.g., if two equal point masses are separated by certain distance, the centre of mass lies at the mid point of two point masses and there is no mass at that point.
730 Views

What is the significance of defining the center of mass of a system?

The motion of n particle system can be reduced to one particle motion.

An equivalent single point object would enable us to discuss the overall motion of the system. 
794 Views

What is the need of centre of mass?

Newton’s second law of motion is strictly applicable to point masses only. To apply the Newton's law of motion to rigid bodies, the concept of centre of mass is introduced.

The concept of centre of mass of a system enables us to discuss overall motion of the system by replacing the system by an equivalent single point object. 
911 Views

Define centre of mass.

Centre of mass of a body or a system of bodies is a point at which the entire mass of the body or system is supposed to be concentrated. 
1449 Views

Is it necessary for centre of mass to lie within the body?

No, centre of mass needs not to lie within the body. It is not necessary that the total mass of the system be actually present at the centre.

The position of the centre of mass is calculated using the usual Newtonian type of equations of motion. 
943 Views