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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

From a circular disc of radius R and mass 9M, a small disc of mass M and radius R/3 is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is

  • 40MR2/9

  • MR2

  • 4 MR2

  • 4MR2/9


A.

40MR2/9

The moment of inertia of the remaining disc about axis perpendicular to the plane of the disc and passing through its centre.


straight I space equals space straight I subscript 1 minus straight I subscript italic 2
space equals fraction numerator 9 MR squared over denominator 2 end fraction minus MR squared over 18
equals space fraction numerator 81 space MR squared minus MR squared over denominator 18 end fraction
equals space fraction numerator 40 space MR squared over denominator 9 end fraction

The moment of inertia of the remaining disc about axis perpendicular to the plane of the disc and passing through its centre.


straight I space equals space straight I subscript 1 minus straight I subscript italic 2
space equals fraction numerator 9 MR squared over denominator 2 end fraction minus MR squared over 18
equals space fraction numerator 81 space MR squared minus MR squared over denominator 18 end fraction
equals space fraction numerator 40 space MR squared over denominator 9 end fraction

2046 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 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

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

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