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A rod of length ' l' is standing vertically on smooth horizontal surface. It is disturbed slightly so that lower end turns towards step. Angular speed of rod just after hitting step is (end of rod sticks to step)

A rod of length ' l' is standing vertically
on smooth horizontal surface. It is
disturbed slightly so that lower end turns
towards step. Angular speed of rod just
after hitting step is (end of rod sticks to
step)

Question Image
Grade:12

1 Answers

Arun
25750 Points
3 years ago
Suppose mass of rod be M, and at a certain time, it makes angle θ with the vertical.
The only force acting on the rod is its own weight, which provides a torque about point O,
τ=Mg 
2
L
​ 
 sinθ
Moment of inertia of rod about I is:
C
​ 
 = 
3
ML 
2
 
​ 
 
During rotation, we have:-
τ=Iα, and for point O:
Mg 
2
L
​ 
 sinθ= 
3
ML 
2
 
​ 
 α
⇒α= 
2L
3gsinθ
​ 
 
Hence centre of mass has an acceleration:
CM
​ 
 =Rα, where R= 
2
L
​ 
  gives a 
CM
​ 
 = 
4
3
​ 
 gsinθ.

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