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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

Four identical thin rods each of mass M and length l , inertial form a square frame. moment of inertia of this frame about an axis through the centre of the square and perpendicular to this plane is 

  • 4Ml2/3

  • 2Ml2/3

  • 13Ml2/3

  • Ml2/3


A.

4Ml2/3

Apply theorem of the parallel axis and the total moment of inertia will be the sum of the moment of inertia of each rod.
Moment of inertia of rod about an axis through its centre of mass and perpendicular to rod + (mass) of rod) x (perpendicular distance between two axes)


MI squared over 12 space plus space M open parentheses l over 2 close parentheses squared space equals space open parentheses fraction numerator M I squared over denominator 3 end fraction close parentheses
M o m e n t space o f space i n e r t i a space o f space t h e space s y s t e m space space equals space fraction numerator M l cubed space over denominator 3 end fraction x space 4
space equals space 4 over 3 space M l squared

Apply theorem of the parallel axis and the total moment of inertia will be the sum of the moment of inertia of each rod.
Moment of inertia of rod about an axis through its centre of mass and perpendicular to rod + (mass) of rod) x (perpendicular distance between two axes)


MI squared over 12 space plus space M open parentheses l over 2 close parentheses squared space equals space open parentheses fraction numerator M I squared over denominator 3 end fraction close parentheses
M o m e n t space o f space i n e r t i a space o f space t h e space s y s t e m space space equals space fraction numerator M l cubed space over denominator 3 end fraction x space 4
space equals space 4 over 3 space M l squared

2228 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