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Instantaneous center of a body rolling with sliding on a stationary curved surface lies
a)at the point of contact
b)on the common normal at the point of contact
c)on the common tangent at the point of contact
d)at the centre of curvature of the stationary surface
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Instantaneous center of a body rolling with sliding on a stationary cu...
Answer will be A only if sliding is not there and body is purely rolling but in this case answer should be B as sliding occurs.
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Instantaneous center of a body rolling with sliding on a stationary cu...
Explanation:
The instantaneous center of a rolling body is a point on the body that has zero velocity at any instant of time. In the case of a rolling body with sliding on a stationary curved surface, the instantaneous center lies on the common normal at the point of contact between the body and the surface.
Why is the instantaneous center on the common normal?
When a body rolls with sliding on a stationary curved surface, the two points of contact between the body and the surface have different velocities. The point of contact on the front side of the body has a higher velocity than the point of contact on the rear side of the body. This difference in velocity causes a relative sliding motion between the body and the surface.
To understand why the instantaneous center lies on the common normal, consider the following:
- At the point of contact, the body and the surface have the same velocity.
- At any other point on the body, the velocity is not zero.
- Therefore, there must be a point on the body where the velocity is zero.
- This point is the instantaneous center.
- Since the body is rolling with sliding, the instantaneous center must lie on the common normal at the point of contact.
Why not on the common tangent or at the center of curvature?
- The common tangent at the point of contact is the line that is tangent to both the body and the surface at the point of contact. This line does not have zero velocity, so the instantaneous center cannot lie on it.
- The center of curvature of the stationary surface is a fixed point that does not change with the motion of the body. The instantaneous center, on the other hand, is a point that moves with the motion of the body. Therefore, the instantaneous center cannot be at the center of curvature.
Conclusion:
The instantaneous center of a body rolling with sliding on a stationary curved surface lies on the common normal at the point of contact between the body and the surface. This is because the instantaneous center is the point on the body that has zero velocity at any instant of time, and the common normal is the only line that has zero velocity at the point of contact.
The instantaneous center of a rolling body is a point on the body that has zero velocity at any instant of time. In the case of a rolling body with sliding on a stationary curved surface, the instantaneous center lies on the common normal at the point of contact between the body and the surface.
Why is the instantaneous center on the common normal?
When a body rolls with sliding on a stationary curved surface, the two points of contact between the body and the surface have different velocities. The point of contact on the front side of the body has a higher velocity than the point of contact on the rear side of the body. This difference in velocity causes a relative sliding motion between the body and the surface.
To understand why the instantaneous center lies on the common normal, consider the following:
- At the point of contact, the body and the surface have the same velocity.
- At any other point on the body, the velocity is not zero.
- Therefore, there must be a point on the body where the velocity is zero.
- This point is the instantaneous center.
- Since the body is rolling with sliding, the instantaneous center must lie on the common normal at the point of contact.
Why not on the common tangent or at the center of curvature?
- The common tangent at the point of contact is the line that is tangent to both the body and the surface at the point of contact. This line does not have zero velocity, so the instantaneous center cannot lie on it.
- The center of curvature of the stationary surface is a fixed point that does not change with the motion of the body. The instantaneous center, on the other hand, is a point that moves with the motion of the body. Therefore, the instantaneous center cannot be at the center of curvature.
Conclusion:
The instantaneous center of a body rolling with sliding on a stationary curved surface lies on the common normal at the point of contact between the body and the surface. This is because the instantaneous center is the point on the body that has zero velocity at any instant of time, and the common normal is the only line that has zero velocity at the point of contact.
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Instantaneous center of a body rolling with sliding on a stationary curved surface liesa)at the point of contactb)on the common normal at the point of contactc)on the common tangent at the point of contactd)at the centre of curvature of the stationary surfaceCorrect answer is option 'B'. Can you explain this answer?
Question Description
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Instantaneous center of a body rolling with sliding on a stationary curved surface liesa)at the point of contactb)on the common normal at the point of contactc)on the common tangent at the point of contactd)at the centre of curvature of the stationary surfaceCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Instantaneous center of a body rolling with sliding on a stationary curved surface liesa)at the point of contactb)on the common normal at the point of contactc)on the common tangent at the point of contactd)at the centre of curvature of the stationary surfaceCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Instantaneous center of a body rolling with sliding on a stationary curved surface liesa)at the point of contactb)on the common normal at the point of contactc)on the common tangent at the point of contactd)at the centre of curvature of the stationary surfaceCorrect answer is option 'B'. Can you explain this answer?.
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