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The system shown in the figure consists of block A of mass 5 kg connected to a spring through a massless rope passing over pulley B of radius r and mass 20 kg. The spring constant k is 1500 N/m. If there is no slipping of the rope over the pulley, the natural frequency of the system is _______ rad/s.
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- 0.01 rad /sec
- 10 rad /sec
- 100 rad /sec
- 110 rad /sec
Correct Option: B
| KE = | m ẋ2 + | I θ̇2 | ||
| 2 | 2 |
| m = 5 kg , θ = | ||
| r |
| I = | = 10r2 | |
| 2 |
| KE = | 5 ẋ2 + | 10r2 . | = | (15) ẋ2 | ||||
| 2 | 2 | r2 | 2 |
∴ meq = 15
| PE = | kx2 | |
| 2 |
∴ keq = k = 1500 N / m
Natural frequency
= 10 rad /sec
