Circular Motion probem - 3

In summary, the problem involves determining the acceleration of a particle moving in a circle at constant angular speed. The solution involves drawing free-body diagrams for each mass and considering the net force acting on each particle. By setting up equations for the tensions in the strings and using the length of each string segment, the desired ratio can be found.

The problem is as such :

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Attempt to the problem:

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The answer is confusing Option D

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Tension is a force and force is related to acceleration via Newton's 2nd law. How do you determine the acceleration of a particle moving in a circle at constant angular speed ##\omega##?

Draw free-body diagrams for each mass. You need to consider the NET force acting on each particle.

TSny said:
Draw free-body diagrams for each mass. You need to consider the NET force acting on each particle.
But friend how could it be done without knowing the separations.

If we draw the free body diagram there would be two accelerations - tangential aT and centripetal aR

aR will be along the thread and it will equate the tension. Isn't it?

TSny said:
Draw free-body diagrams for each mass. You need to consider the NET force acting on each particle.

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If we draw the free body diagram there would be two accelerations - tangential aT and centripetal aR

Since the only forces acting on the particles are tensions which are radial ,there will be no tangential acceleration.

The FBD in the above post#4 is incorrect.

Let the tension in the string OA be T1,AB be T2 and BC be T3.The length of each string segment be l.

Now for A, T1-T2=mv12/l

For B ,T2-T3=mv22/2l

Similarly you can write eq for C.

From this you will get the desired ratio.

Thank you very much friends. I got the answer. Problem has been cleared.

What is circular motion?

Circular motion is a type of motion in which an object moves along a circular path at a constant speed. This motion can be either uniform, where the speed remains constant, or non-uniform, where the speed varies at different points along the path.

What is centripetal force?

Centripetal force is the force that acts on an object moving in a circular path, directed towards the center of the circle. It is responsible for keeping the object in its circular motion and preventing it from flying off in a straight line.

How is centripetal force calculated?

The magnitude of centripetal force can be calculated using the formula Fc = mv^2/r, where m is the mass of the object, v is the velocity, and r is the radius of the circular path.

What is the difference between centripetal and centrifugal force?

Centripetal force is the inward force that keeps an object in circular motion, while centrifugal force is the outward force that appears to push an object away from the center of the circle. However, centrifugal force is actually a fictitious force that only appears due to the inertia of the object.

How is circular motion related to Newton's laws of motion?

Circular motion is governed by Newton's laws of motion, specifically the first law which states that an object will continue to move in a straight line at a constant speed unless acted upon by an external force. In circular motion, the centripetal force acts as the external force that keeps the object moving in a circular path.