I have 2 questions where I have some difficulty in the solution method shown in the books.
In case of the question number 5 I DONOT understand why there is an $mga cos \theta$ in the equation of potential energy.
Next
Here in the above question I think there should one more term $ mgl sin\alpha$ in the equation of V.
Please let me know if I an erring in any of the questions.
To the first doubt, the potential energy with reference to the horizontal plane, is given by the height of the cylinder center regarding the base plane. This height is composed of two terms: first the height of the contact point which is $(s-x)\sin\theta$ and the other $a \cos\theta$ which is the cylinder center elevation regarding the point of contact. Then
$$ V = \left((s-x)\sin\theta + a\cos\theta\right)mg $$