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Question

A mass is supported on a frictionless horizontal surface. It is attached to a string and rotates fixed center at an angular velocity ω0 . If the length of the string and angular velocity both are doubled, the tension in the string which was initially T0 is now​


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Solution

Step 1. Given data:

Initial angular velocity = ω0

Initial tension in the string = T0

Final length L= 2×Initial lengthL0

Final angular velocity ω= 2×initial angular velocityω0

Let final tension in the string = T

Step 2. Formula used:

T=mω2L

Where m= mass.

Step 3. Calculations:

According to the question, putting the given values, we get

T=m2ω02.2L0=8mω02.L0T=8T0

Thus, the final tension will become eight times the initial tension.


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