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Two particles of equal mass are moving along x-axis and y-axis respectively, if initial velocity of 1st particle is zero but acceleration is constant whereas 2nd particle acceleration is zero, then path of centre of mass
- a)Straight line
- b)Parabolic
- c)Circle
- d)Other curvature path
Correct answer is option 'B'. Can you explain this answer?
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Two particles of equal mass are moving along x-axis and y-axis respec...
x ∝ y2, path is parabolic.
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Two particles of equal mass are moving along x-axis and y-axis respec...
The path of the center of mass of the two particles can be determined by considering the individual motions of each particle.
1. Particle 1:
- Particle 1 has an initial velocity of zero, which means it starts from rest.
- However, it has a constant acceleration. This implies that it will undergo uniformly accelerated motion.
- The path of particle 1 will be a parabolic curve, as it is the path followed by an object under constant acceleration starting from rest.
2. Particle 2:
- Particle 2 has an acceleration of zero, which means its velocity remains constant throughout its motion.
- Since the acceleration is zero, the velocity-time graph will be a straight line parallel to the time axis.
- The path of particle 2 will be a straight line along the y-axis.
Center of Mass:
The center of mass of a system of particles is the point where the average position of all the particles is considered to be concentrated.
In this case, since both particles have equal mass, the center of mass will lie exactly halfway between them.
Considering particle 1's parabolic path and particle 2's straight line path, the center of mass will also follow a parabolic path.
This can be understood by visualizing the situation:
- As particle 1 moves along its parabolic path, the center of mass will shift accordingly.
- At any given time, the center of mass will be at the midpoint between the two particles.
- Since particle 2 moves in a straight line, the midpoint between the two particles will also move along a straight line, parallel to the y-axis.
- However, the combined motion of particle 1 and particle 2 will result in the center of mass following a parabolic path.
Hence, the correct answer is option 'B' - the path of the center of mass will be a parabolic curve.
1. Particle 1:
- Particle 1 has an initial velocity of zero, which means it starts from rest.
- However, it has a constant acceleration. This implies that it will undergo uniformly accelerated motion.
- The path of particle 1 will be a parabolic curve, as it is the path followed by an object under constant acceleration starting from rest.
2. Particle 2:
- Particle 2 has an acceleration of zero, which means its velocity remains constant throughout its motion.
- Since the acceleration is zero, the velocity-time graph will be a straight line parallel to the time axis.
- The path of particle 2 will be a straight line along the y-axis.
Center of Mass:
The center of mass of a system of particles is the point where the average position of all the particles is considered to be concentrated.
In this case, since both particles have equal mass, the center of mass will lie exactly halfway between them.
Considering particle 1's parabolic path and particle 2's straight line path, the center of mass will also follow a parabolic path.
This can be understood by visualizing the situation:
- As particle 1 moves along its parabolic path, the center of mass will shift accordingly.
- At any given time, the center of mass will be at the midpoint between the two particles.
- Since particle 2 moves in a straight line, the midpoint between the two particles will also move along a straight line, parallel to the y-axis.
- However, the combined motion of particle 1 and particle 2 will result in the center of mass following a parabolic path.
Hence, the correct answer is option 'B' - the path of the center of mass will be a parabolic curve.
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Two particles of equal mass are moving along x-axis and y-axis respectively, if initial velocity of 1st particle is zero but acceleration is constant whereas 2nd particle acceleration is zero, then path of centre of massa) Straight lineb) Parabolicc) Circled) Other curvature pathCorrect answer is option 'B'. Can you explain this answer?
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