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A particle is moving with one component of constant velocity parallel to the axis of y and another component of velocity parallel to the axis of x proportional to y. It will describe a
- a)Circle
- b)parabola
- c)spiral
- d)catenary
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A particle is moving with one component of constant velocity parallel ...
When a body is moving parallel to the axis of y and moving parallel to x-axis then it's intersecting point is like a parabola.
A particle moving with one component of constant velocity parallel to the y-axis and another component of velocity parallel to the x-axis proportional to y will describe a parabola. This is because the y component of velocity is constant, meaning the vertical motion of the particle is a simple linear motion, and the x component of velocity is proportional to y, meaning the horizontal motion of the particle is a quadratic function of y. The combination of these two motions results in a parabolic path.
A circle is a closed curved path which is defined by all points that are equidistant from a center point. In this case, the particle doesn't move in a closed curved path but rather in a parabolic shape.
A spiral is a curve that starts from a central point and gradually moves away from it. It is a non-closed path that loops around the central point. In this case, the particle doesn't move in a spiral shape but rather in a parabolic shape.
A catenary is the shape formed by a hanging chain or cable. It is defined by the weight of the chain or cable, as well as its tension. In this case, the particle doesn't move in a catenary shape but rather in a parabolic shape.
Most Upvoted Answer
A particle is moving with one component of constant velocity parallel ...
Explanation:
To understand why the particle will describe a parabolic path, let's break down the components of velocity and analyze the motion.
Given Information:
- One component of velocity is constant and parallel to the y-axis.
- The other component of velocity is proportional to y and parallel to the x-axis.
Analysis:
1. Constant Velocity Component (Vy):
- Since the velocity component parallel to the y-axis is constant, the particle will move with a constant velocity in the y-direction.
- This implies that the particle will move along a straight line parallel to the y-axis.
2. Proportional Velocity Component (Vx):
- The velocity component parallel to the x-axis is proportional to y.
- This means that as the particle moves in the y-direction, its velocity in the x-direction also increases or decreases proportionally.
- The velocity in the x-direction will be positive for positive values of y and negative for negative values of y.
Combined Motion:
1. Initially:
- At the starting point, the particle has no velocity in the x-direction (Vx = 0).
- The particle only moves with a constant velocity in the y-direction (Vy).
2. As y increases:
- As the particle moves in the positive y-direction, the velocity in the x-direction (Vx) also increases proportionally.
- This causes the particle to deviate from its initial straight-line path parallel to the y-axis.
- The particle starts curving towards the positive x-direction.
3. As y decreases:
- As the particle moves in the negative y-direction, the velocity in the x-direction (Vx) decreases proportionally.
- This causes the particle to deviate from its initial straight-line path and curve towards the negative x-direction.
Conclusion:
Based on the analysis, it can be concluded that the particle will follow a curved path due to the proportional velocity component parallel to the x-axis. This curved path is a parabola.
Hence, the correct answer is option 'B' - parabola.
To understand why the particle will describe a parabolic path, let's break down the components of velocity and analyze the motion.
Given Information:
- One component of velocity is constant and parallel to the y-axis.
- The other component of velocity is proportional to y and parallel to the x-axis.
Analysis:
1. Constant Velocity Component (Vy):
- Since the velocity component parallel to the y-axis is constant, the particle will move with a constant velocity in the y-direction.
- This implies that the particle will move along a straight line parallel to the y-axis.
2. Proportional Velocity Component (Vx):
- The velocity component parallel to the x-axis is proportional to y.
- This means that as the particle moves in the y-direction, its velocity in the x-direction also increases or decreases proportionally.
- The velocity in the x-direction will be positive for positive values of y and negative for negative values of y.
Combined Motion:
1. Initially:
- At the starting point, the particle has no velocity in the x-direction (Vx = 0).
- The particle only moves with a constant velocity in the y-direction (Vy).
2. As y increases:
- As the particle moves in the positive y-direction, the velocity in the x-direction (Vx) also increases proportionally.
- This causes the particle to deviate from its initial straight-line path parallel to the y-axis.
- The particle starts curving towards the positive x-direction.
3. As y decreases:
- As the particle moves in the negative y-direction, the velocity in the x-direction (Vx) decreases proportionally.
- This causes the particle to deviate from its initial straight-line path and curve towards the negative x-direction.
Conclusion:
Based on the analysis, it can be concluded that the particle will follow a curved path due to the proportional velocity component parallel to the x-axis. This curved path is a parabola.
Hence, the correct answer is option 'B' - parabola.
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Community Answer
A particle is moving with one component of constant velocity parallel ...
When a body is moving parallel to the axis of y and moving parallel to x-axis then it's intersecting point is like a parabola.
A particle moving with one component of constant velocity parallel to the y-axis and another component of velocity parallel to the x-axis proportional to y will describe a parabola. This is because the y component of velocity is constant, meaning the vertical motion of the particle is a simple linear motion, and the x component of velocity is proportional to y, meaning the horizontal motion of the particle is a quadratic function of y. The combination of these two motions results in a parabolic path.
A circle is a closed curved path which is defined by all points that are equidistant from a center point. In this case, the particle doesn't move in a closed curved path but rather in a parabolic shape.
A spiral is a curve that starts from a central point and gradually moves away from it. It is a non-closed path that loops around the central point. In this case, the particle doesn't move in a spiral shape but rather in a parabolic shape.
A catenary is the shape formed by a hanging chain or cable. It is defined by the weight of the chain or cable, as well as its tension. In this case, the particle doesn't move in a catenary shape but rather in a parabolic shape.
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A particle is moving with one component of constant velocity parallel to the axis of y and another component of velocity parallel to the axis of x proportional to y. It will describe aa)Circleb)parabolac)spirald)catenaryCorrect answer is option 'B'. Can you explain this answer?
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