﻿ A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to origin O is LA when it is at A and LB when it is B, then:  from Physics System of Particles and Rotational Motion Class 11 Manipur Board

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A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to origin O is LA when it is at A and LB when it is B, then:

• LA > LB

• LA = LB

• the relationship between LA and LB depends upon the slope of the line AB

• LA < LB

B.

LA = LB

From the definition of angular momentum,

Therefore, the magnitude of L is
L = mvr sin Φ = mvd

where d = r sin Φ is the distance of closest approach of the particle so the origin. As d is same for both the particles, hence, LA = LB

From the definition of angular momentum,

Therefore, the magnitude of L is
L = mvr sin Φ = mvd

where d = r sin Φ is the distance of closest approach of the particle so the origin. As d is same for both the particles, hence, LA = LB

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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.

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Is it necessary that there should be matter at the centre of mass of system?

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Is it necessary for centre of mass to lie within the body?

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