Homework Help: Bead sliding on hemisphere

Tags:
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.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted