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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

Three identical spherical shells, each of mass m and radius r are placed as shown in the figure. Consider an axis XX', which is touching to two shells and passing through the diameter of the third shell. Moment of inertia of the system consisting of these three spherical shells about XX' axis is

  • 11/5 mr2

  • 3 mr2

  • 16/5 mr2

  • 4 mr2


D.

4 mr2

The total moment of inertia of the system is 


I = I1 +I2 +I3
Here comma space straight I subscript 1 space equals space 2 over 3 space mr squared
straight I subscript 2 space equals space straight I subscript 3 space equals space 2 over 3 mr squared space plus mr squared space left square bracket space From space parallel space axis space theorem right square bracket
space equals space 5 over 3 space mr squared
space fro space eq space left parenthesis straight i right parenthesis space
straight I space equals space 2 over 3 space mr squared space plus 2 space straight x space 5 over 3 space mr squared space equals mr squared open parentheses 2 over 3 plus 10 over 3 close parentheses
straight I space equals space 4 mr squared

The total moment of inertia of the system is 


I = I1 +I2 +I3
Here comma space straight I subscript 1 space equals space 2 over 3 space mr squared
straight I subscript 2 space equals space straight I subscript 3 space equals space 2 over 3 mr squared space plus mr squared space left square bracket space From space parallel space axis space theorem right square bracket
space equals space 5 over 3 space mr squared
space fro space eq space left parenthesis straight i right parenthesis space
straight I space equals space 2 over 3 space mr squared space plus 2 space straight x space 5 over 3 space mr squared space equals mr squared open parentheses 2 over 3 plus 10 over 3 close parentheses
straight I space equals space 4 mr squared

2956 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

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

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 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 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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