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The assembly shown in the figure is composed of two massless rods of length l with two particles, each of mass m. The natural frequency of this assembly for small oscillations is
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- √g / l
- √2g / l(cosα)
- √g / l(cosα)
- √(gcosα) / l
- √g / l
Correct Option: D
Net restoring torque when displaced by a small angle θ
τ = mg cos (α – θ) l – mg (α + θ)l
= 2 mgl cos α sin θ
For very small θ, sin θ ≈ θ
∴ τ = 2mgl cos α . θ (restorative)
| Now , I | + 2mgl cosα . θ = 0 | |
| dt2 |
But I = 2ml2
| ∴ 2ml2 | + 2mgl cosα . θ = 0 | |
| dt2 |
| or | + | θ = 0 | ||
| dt2 | l |
| ∴ ωn = √ | ||
| l |
