Answer:
2440.24 J
Explanation:
Moment of inertia, I1 = 5 kg m^2
frequency, f1 = 3 rps
ω1 = 2 x π x f1 = 2 x π x 3 = 6 π rad/s
Moment of inertia, I2 = 2 kg m^2
Let the new frequency is f2.
ω2 = 2 x π x f2
here no external torque is applied, so the angular momentum remains constant.
I1 x ω1 = I2 x ω2
5 x 6 π = 2 x 2 x π x f2
f2 = 7.5 rps
ω2 = 2 x π x 7.5 = 15 π
Initial kinetic energy, K1 = 1/2 x I1 x ω1^2 = 0.5 x 5 x (6 π)² = 887.36 J
Final kinetic energy, K2 = 1/2 x I2 x ω2^2 = 0.5 x 3 x (15 π)² = 3327.6 J
Work done, W = Change in kinetic energy = 3327.6 - 887.36 = 2440.24 J
The exercise is related to the Ratio Test for Convergence. The rules for this kind of test are given below.
<h3>What are the rules for Ratio Test for Convergence?</h3>
The rules are:
- If the limit is less than 1 when conducting the ratio test, your series is definitely convergent.
- The test is inconclusive if the limit is equal to 1.
- The series is divergent if the limit is greater than 1.
Using this knowledge, we are able to state that
- A is not conclusive.
- C's convergence is absolute.
- There is divergence with D and E.
- B and F appear to be employing the nth-term test. The nth-term involves determining the sequence's limit as it approaches infinity.
The nth-term test determines whether a series is divergent if the limit is bigger than 0, thus, both B and F are divergent series.
Please see the attached for the full question and the link below for more about Ratio Test for Convergence:
brainly.com/question/16618162
