A force of  acts on O, the origin of the coordinate system. The torque about the point (1, −1) is from Physics System of Particles and Rotational Motion Class 11 Manipur Board
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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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A force of negative straight F straight k with hat on top acts on O, the origin of the coordinate system. The torque about the point (1, −1) is

  • negative straight F left parenthesis straight i with hat on top space minus straight j with hat on top right parenthesis
  • straight F left parenthesis straight i with hat on top space minus straight j with hat on top right parenthesis
  • negative straight F left parenthesis straight i with hat on top space plus straight j with hat on top right parenthesis
  • straight F left parenthesis straight i with hat on top space plus straight j with hat on top right parenthesis

C.

negative straight F left parenthesis straight i with hat on top space plus straight j with hat on top right parenthesis
straight tau with rightwards arrow on top space equals space left parenthesis negative straight i with hat on top plus straight j with hat on top right parenthesis space straight x space left parenthesis negative straight F straight k with hat on top right parenthesis
equals negative straight F space left parenthesis straight i with hat on top space plus straight j with hat on top right parenthesis
straight tau with rightwards arrow on top space equals space left parenthesis negative straight i with hat on top plus straight j with hat on top right parenthesis space straight x space left parenthesis negative straight F straight k with hat on top right parenthesis
equals negative straight F space left parenthesis straight i with hat on top space plus straight j with hat on top right parenthesis
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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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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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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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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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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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