A uniform rod AB of length l and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A  is ml2/3, the initial angular acceleration of the rod will be: from Physics System of Particles and Rotational Motion Class 11 Manipur Board
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A uniform rod AB of length l and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A  is ml2/3, the initial angular acceleration of the rod will be:

  • 2g/3l

  • mgl/2

  • 3gl/2

  • 3g/2l


D.

3g/2l

The moment of inertia of the uniform rod about an axis through one end and perpendicular to its length is 

l = ml3/3

where m is a mass of rod and l is the

straight tau space equals space mg straight iota over 2
Iα space equals space mg straight l over 2
ml squared over 3 straight alpha space equals space mg straight l over 2
straight alpha space equals space fraction numerator 3 straight g over denominator 2 straight l end fractionlength.

Torque acting on centre of gravity of rod is given by

The moment of inertia of the uniform rod about an axis through one end and perpendicular to its length is 

l = ml3/3

where m is a mass of rod and l is the

straight tau space equals space mg straight iota over 2
Iα space equals space mg straight l over 2
ml squared over 3 straight alpha space equals space mg straight l over 2
straight alpha space equals space fraction numerator 3 straight g over denominator 2 straight l end fractionlength.

Torque acting on centre of gravity of rod is given by

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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.
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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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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. 
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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. 
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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. 
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