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A uniform rod of length L is suspended from one end such that it is free to rotate about an axis passing through that end and perpendicular to the length, what maximum speed must be imparted to the lower end so that the rod completes one full revolution? 

(A) √(2gL) 

(B) 2√(gL) 

(C) √(6gL) 

(D) 2√(2gL)

1 Answer

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Best answer

Correct option: (C) (6gL)

Explanation:

In one full revolution the increase in P.E = MgL, (L = length of rod, M = is the mass of rod)

By conservation of energy,

MgL = (1/2)Iω2 

for rod, I = (ML2 / 3)

hence

MgL = (1/2) × (ML2 / 3) × ω2 

g = (1/6)Lω2 

ω2 = (6g / L)

Velocity = V = r × ω

here r = L

hence

V = Lω

= L × √(6g / L)

(6gL)  

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