Mechanics Booster-7

1 Answers

Sourish Ghosh ·

Let the reference point be intersection of the wall and the floor, call it 'O'.
Note: the locus of the COM of the rod is a circle of radius l/2.

Conserving energy about O,
mgl2(1 - cosθ) = 12mv2 + 12Icomw2
w = 2vl
v = √[3gl(1 - cosθ)4]

Now vx = vcosθ
As θ increases, vx acquires a local maximum, and then it decreases.
In short,
dvxdθ > 0, θ < cos-1(2/3)
dvxdθ < 0, θ > cos-1(2/3)

Normal reaction was from the wall was acting to the right till θ = cos-1(2/3) increasing the velocity. When θ > cos-1(2/3), vx starts decreasing => normal reaction is acting to the left which is impossible. Hence it loses contact at that angle.

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