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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

A thin rod of length L and Mass M is bent at its midpoint into two halves so that the angle between them is 90o. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is 

  • ML2/24

  • ML2/12

  • ML2/6

  • fraction numerator square root of 2 space ML squared over denominator 24 end fraction

B.

ML2/12

Since rod is bent at the middle, so each part of it will have same length (L/2) and mass (M/2) as shown,


Moment of inertia of each part through its one end

 equals space 1 third open parentheses straight M over 2 close parentheses open parentheses straight L over 2 close parentheses squared
Hence, net moment of inertia through its middle point O is

straight I space equals space 1 third open parentheses straight M over 2 close parentheses open parentheses straight L over 2 close parentheses squared space plus 1 third open parentheses straight M over 2 close parentheses open parentheses straight L over 2 close parentheses squared
equals 1 third open square brackets ML squared over 8 plus ML squared over 8 close square brackets space equals space ML squared over 12

Since rod is bent at the middle, so each part of it will have same length (L/2) and mass (M/2) as shown,


Moment of inertia of each part through its one end

 equals space 1 third open parentheses straight M over 2 close parentheses open parentheses straight L over 2 close parentheses squared
Hence, net moment of inertia through its middle point O is

straight I space equals space 1 third open parentheses straight M over 2 close parentheses open parentheses straight L over 2 close parentheses squared space plus 1 third open parentheses straight M over 2 close parentheses open parentheses straight L over 2 close parentheses squared
equals 1 third open square brackets ML squared over 8 plus ML squared over 8 close square brackets space equals space ML squared over 12

2690 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 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

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

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. 
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