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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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When a string is divided into three segments of length l1, l2, and l3 the fundamental frequencies of these three segments are v1, v2, and v3 respectively. The original fundamental frequency (v) of the string is

  • square root of straight v space equals space square root of v subscript 1 end root plus square root of v subscript 2 end root plus square root of v subscript 3 end root
  • v = v1 +v2 +v3

  • 1 over straight v space equals space 1 over v subscript 1 space plus 1 over v subscript 2 plus 1 over v subscript 3
  • fraction numerator 1 over denominator square root of straight v end fraction space equals space fraction numerator 1 over denominator square root of v subscript 1 end root end fraction plus fraction numerator 1 over denominator square root of v subscript 2 end root end fraction plus 1 over square root of v subscript 3

C.

1 over straight v space equals space 1 over v subscript 1 space plus 1 over v subscript 2 plus 1 over v subscript 3

The fundamental frequency of string

straight v equals space fraction numerator 1 over denominator 2 straight l end fraction square root of straight T over straight m end root
straight v subscript 1 straight l subscript 1 space equals straight v subscript 2 straight l subscript 2 space equals space straight v subscript 3 straight l subscript 3 space equals space straight k
From space eq space left parenthesis straight i right parenthesis
straight l subscript 1 space equals space straight k over straight v subscript 1 comma space straight l subscript 2 space equals space straight k over straight v subscript 2 comma straight l subscript 3 space equals space straight k over straight v subscript 3
original space length
straight l equals straight k over straight v
Here comma space straight l equals straight l subscript 1 plus straight l subscript 2 plus straight l subscript 3
straight k over straight v space equals straight k subscript 1 over straight v subscript 1 space plus straight k subscript 2 over straight v subscript 2 plus straight k subscript 3 over straight v subscript 3
1 over straight v space equals 1 over straight v subscript 1 space plus 1 over straight v subscript 2 plus 1 over straight v subscript 3

The fundamental frequency of string

straight v equals space fraction numerator 1 over denominator 2 straight l end fraction square root of straight T over straight m end root
straight v subscript 1 straight l subscript 1 space equals straight v subscript 2 straight l subscript 2 space equals space straight v subscript 3 straight l subscript 3 space equals space straight k
From space eq space left parenthesis straight i right parenthesis
straight l subscript 1 space equals space straight k over straight v subscript 1 comma space straight l subscript 2 space equals space straight k over straight v subscript 2 comma straight l subscript 3 space equals space straight k over straight v subscript 3
original space length
straight l equals straight k over straight v
Here comma space straight l equals straight l subscript 1 plus straight l subscript 2 plus straight l subscript 3
straight k over straight v space equals straight k subscript 1 over straight v subscript 1 space plus straight k subscript 2 over straight v subscript 2 plus straight k subscript 3 over straight v subscript 3
1 over straight v space equals 1 over straight v subscript 1 space plus 1 over straight v subscript 2 plus 1 over straight v subscript 3

2075 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. 
911 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