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a uniform chain of length πr lies inside a smooth semicircle tube AB radius R.assuming that slight disturbance to start the chain in motion the velocity with which it will emerge from the end will be

a uniform chain of length πr lies inside a smooth semicircle tube AB radius R.assuming that slight disturbance to start the chain in motion the velocity with which it will emerge from the end will be

Grade:12th pass

1 Answers

Sachin Kumar
10 Points
one year ago

Since it is an elongated body of mass M(let)

Let's assume a small mass dm at angle x with

angle dx.

Now mass per unit x will be M/π.dx

dU=dmgh

      = (M/π)grsinxdx

Integrating wrt X from angle 0 to π

U=2mgr/π

 

All forces are conservative

Hence 

Ki+Hi=Kf+Uf…….i

 

 

But Uf=mgr(π/2)

Since h=r(π/2)

 

Now from i

2mgr/π=mv^2/2+mgr(π/2)

v=   √ 2gr(2/π+π/2)



 

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