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A particle of mass M is moving in a horizontal circle of radius R with uniform speed V. When it moves from one point to a diametrically opposite point, its [1992]
- a)kinetic energy changes by MV2/4
- b)momentum does not change
- c)momentum changes by 2 MV
- d)kinetic energy changes by MV2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A particle of mass M is moving in a horizontal circle of radius R with...
On the diametrically opposite points, the velocities have same magnitude but opposite directions. Therefore, change in momentum is MV – (– MV) = 2MV
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A particle of mass M is moving in a horizontal circle of radius R with...
Given information:
- Particle of mass M
- Moving in a horizontal circle of radius R
- Uniform speed V
To understand the change in momentum and kinetic energy of the particle when it moves from one point to a diametrically opposite point, let's analyze the situation step by step.
Impact of Circular Motion:
When an object moves in a circle, it experiences a centripetal force that keeps it in the circular path. In this case, the centripetal force is provided by the tension force in the string or any other force acting towards the center of the circle.
Change in Position:
When the particle moves from one point to a diametrically opposite point, its position changes. As a result, its velocity vector changes because velocity is a vector quantity that includes both magnitude and direction.
Change in Momentum:
Since velocity changes when the particle moves from one point to another, its momentum will also change. Momentum is defined as the product of mass and velocity. As both mass (M) and velocity (V) remain constant, the momentum of the particle will change as it moves from one point to a diametrically opposite point.
Change in Kinetic Energy:
Kinetic energy is given by the equation KE = (1/2)MV^2. Since the mass (M) and speed (V) remain constant throughout the motion, the kinetic energy of the particle will remain the same. The kinetic energy is not affected by the change in position of the particle within the circular path.
Conclusion:
Based on the above analysis, we can conclude that when the particle moves from one point to a diametrically opposite point in a horizontal circular motion with a uniform speed, its momentum changes by 2MV. The change in momentum is due to the change in velocity of the particle. However, the kinetic energy remains constant as it is not affected by the change in position within the circular path.
- Particle of mass M
- Moving in a horizontal circle of radius R
- Uniform speed V
To understand the change in momentum and kinetic energy of the particle when it moves from one point to a diametrically opposite point, let's analyze the situation step by step.
Impact of Circular Motion:
When an object moves in a circle, it experiences a centripetal force that keeps it in the circular path. In this case, the centripetal force is provided by the tension force in the string or any other force acting towards the center of the circle.
Change in Position:
When the particle moves from one point to a diametrically opposite point, its position changes. As a result, its velocity vector changes because velocity is a vector quantity that includes both magnitude and direction.
Change in Momentum:
Since velocity changes when the particle moves from one point to another, its momentum will also change. Momentum is defined as the product of mass and velocity. As both mass (M) and velocity (V) remain constant, the momentum of the particle will change as it moves from one point to a diametrically opposite point.
Change in Kinetic Energy:
Kinetic energy is given by the equation KE = (1/2)MV^2. Since the mass (M) and speed (V) remain constant throughout the motion, the kinetic energy of the particle will remain the same. The kinetic energy is not affected by the change in position of the particle within the circular path.
Conclusion:
Based on the above analysis, we can conclude that when the particle moves from one point to a diametrically opposite point in a horizontal circular motion with a uniform speed, its momentum changes by 2MV. The change in momentum is due to the change in velocity of the particle. However, the kinetic energy remains constant as it is not affected by the change in position within the circular path.
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A particle of mass M is moving in a horizontal circle of radius R with uniform speed V. When it moves from one point to a diametrically opposite point, its [1992]a)kinetic energy changes by MV2/4b)momentum does not changec)momentum changes by 2 MVd)kinetic energy changes by MV2Correct answer is option 'C'. Can you explain this answer?
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