An object is formed by removing a cylinder of radius $$\(\frac{2}{3} a\)$$ and height $$\(k h(k< 1)\)$$ from a uniform solid cylinder of radius $$\(a\)$$ and height $$\(h\)$$. The vertical axes of symmetry of the two cylinders coincide. The upper faces of the two cylinders are in the same plane as each other. The points $$\(A\)$$ and $$\(B\)$$ are the opposite ends of a diameter of the upper face of the object (see diagram). Find, in terms of $$\(h\)$$ and $$\(k\)$$, the distance of the centre of mass of the object from $$\(A B\)$$. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . When the object is suspended from $$\(A\)$$, the angle between $$\(A B\)$$ and the vertical is $$\(\theta\)$$, where $$\(\tan \theta=\frac{3}{2}\)$$.

Answer:

Knowledge points:

Solution: