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in the following question if we write torque equation as a function of r
then
y(r)=mgr
or y=mx
which is a straight line
after the worm is at rest
y(R)=mgR
y=constant
This way the answer should come as A.
but torque is also=M.O.I*angular acceleration
At final point angular acceleration=0 ,therefore torque should be 0.
therefore on second thinking the answer should be B.
Can you please tell me where am I going wrong.

Vishesh Mangla , 9 Years ago
Grade Select Grade
anser 1 Answers
Askiitians Tutor Team

Last Activity: 14 Days ago

It seems like you're grappling with the concepts of torque, angular acceleration, and how they relate to equilibrium conditions. Let's break this down step by step to clarify the confusion.

Understanding Torque and Equilibrium

Torque (τ) is defined as the product of the force applied and the distance from the pivot point (or axis of rotation) at which the force is applied. Mathematically, it can be expressed as:

Torque (τ) = r × F

Where r is the distance from the pivot point and F is the force applied. In your case, it seems you're considering the torque due to a weight (mg) acting at a distance (R).

Analyzing the Situation

When you mention the equation y(r)=mgr or y=mx, you're essentially describing a linear relationship where the torque increases with the distance from the pivot. This is correct when the system is in motion or when a force is applied. However, when the system reaches a state of rest, the dynamics change.

  • At Rest: When the worm is at rest, the net torque acting on it is zero. This means that all the torques acting on the system must balance out.
  • Torque Equation: If you set up the torque equation at equilibrium, you would have τnet=0. This implies that any applied torque must be countered by an equal and opposite torque.

Angular Acceleration and Torque

Now, regarding the moment of inertia (M.O.I) and angular acceleration, the relationship is given by:

Torque (τ) = I × α

Where I is the moment of inertia and α is the angular acceleration. When the system is at rest, as you correctly pointed out, the angular acceleration α is zero. Thus, the torque must also be zero:

τ = I × 0 = 0

Reconciling the Two Perspectives

Your initial thought process regarding the torque being a function of r is valid, but it applies to the dynamic situation where forces are acting. Once the worm is at rest, the torque indeed becomes zero because the system is in equilibrium. Therefore, the confusion arises from mixing the conditions of motion and rest.

Final Thoughts

In summary, when analyzing the torque in a dynamic situation, you can express it as a function of r. However, when the system is at rest, the torque must equal zero, leading to the conclusion that the answer should reflect the equilibrium condition. This is where your reasoning shifted from A to B. Understanding the context of motion versus rest is crucial in these types of problems.

Feel free to ask if you have more questions or need further clarification on any specific point!

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