What is the Solution to a Confusing Circular Motion Problem?

[thunderhadron]

The problem is as such :



Attempt to the problem:



The answer is confusing Option D

Thank you all in advance.

 

[TSny]

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.

 

[thunderhadron]

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 a_T and centripetal a_R

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

 

[thunderhadron]

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

 

[Tanya Sharma]

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

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.

 

[thunderhadron]

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