A thin rod of length L and mass M is held vertically with one end on the floor and s allowed to fall. Find the velocity of the other end when it hits the floor, assuming that the end on the floor not slip
A
√3gL
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B
√3gL
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C
√L3g
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D
√83L
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Solution
The correct option is A√3gL
On applying the conservation of mechanical energy displacement of centre of mass =L2 , so, Wdone =Δk⋅E⇒mgL2=12Iω2 (I → moment of inertia about end 0
Here, I=ML23 S0, MgL/2=12×mL23⋅ω2⇒ωL=√3gL
Note that, velocity (linear) of end A=ωL=√3gL . So, the correct option is (B).