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In this lesson, we will learn how to find the position of the center of mass of some uniform objects in three dimensions.

Q1:

The uniform solid frustum of a right circular cone is suspended by a string attached to a point on the rim of its smaller circular face. The two circular faces of the frustum have radii 3 cm and 5 cm, and the height of the frustum is 8 cm. Find, to the nearest degree, the angle between the axis of the frustum and the vertical when it hangs in equilibrium.

Q2:

A frustum of a solid right circular cone has circular faces of radii 2 cm and 4 cm and a height of 5 cm. A cylindrical hole of radius 1 cm was bored down the axis of symmetry of the frustum from one circular face to the other. Find the distance between the centre of mass of the solid formed and the centre of its larger face.

Q3:

A uniform solid hemisphere of radius 4 cm and a uniform solid right circular cylinder of height 9 cm and radius 4 cm are joined by their bases to form a composite solid. The centres of the bases coincide at the point π . Given that the hemisphere and the cylinder have the same density, determine the distance between π and the centre of mass of the composite solid.

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