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Bead sliding on hemisphere

  1. Sep 4, 2016 #1
    1. The problem statement, all variables and given/known data
    Capture.PNG
    A bead of mass m kept at the top of a smooth hemispherical wedge of mass M and radius R is gently pushed towards right.As a result,the wedge slides due left.Find the magnitude of velocity of bead relative to the wedge.

    2. Relevant equations
    $$MV=m(v\cos(\theta)-V)$$
    and,

    $$mgR(1-cos(\theta))=(1/2)mv^2+(1/2)MV^2$$ i.e.
    $$mgR(1-cos(\theta))=(1/2)mv^2+(1/2)M(\frac{mvcos(\theta)}{m+M})^2$$

    3. The attempt at a solution

    On solving the two equations I get $$v=\sqrt{\frac{2gR(1-cos(\theta))(m+M)^2}{(M+m)^2+Mm(cos(\theta))^2}}$$

    But this answer is wrong according to my book.Where am I going wrong?
     
  2. jcsd
  3. Sep 4, 2016 #2

    mfb

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    2016 Award

    Staff: Mentor

    How do you define v? You seem to use two different definitions in the first two equations.
     
  4. Sep 4, 2016 #3
    Oh that's my mistake.So in the second equation i should use $$\sqrt{(vcos(\theta)-V)^2+(vsin(\theta))^2}$$ instead of v.Right?
     
  5. Sep 4, 2016 #4

    mfb

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    2016 Award

    Staff: Mentor

    That would make it consistent, yes.
     
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