# Homework Help: Bead sliding on hemisphere

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1. Sep 4, 2016

### Sanchayan Dutta

1. The problem statement, all variables and given/known data

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. Sep 4, 2016

### Staff: Mentor

How do you define v? You seem to use two different definitions in the first two equations.

3. Sep 4, 2016

### Sanchayan Dutta

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?

4. Sep 4, 2016

### Staff: Mentor

That would make it consistent, yes.