A solid hemisphere is mounted on a solid cylinder of same diameter the height of the cylinder being same as its diameter. assuming both the bodies to the made up of the same substance of uniform density, the centre of gravity of the composite system is at the distance in terms of radius r

Aman Bansal
592 Points
12 years ago

Dear Muthu,

In physics, the center of mass or barycenter of a system is the average location of all of its mass. In the case of a rigid body, the position of the center of mass is fixed in relation to the body. In the case of a loose distribution of masses in free space, such as shot from a shotgun or the planets of the Solar System, the position of the center of mass is a point in space among them that may not correspond to the position of any individual mass.
The use of the mass center often allows the use of simplified equations of motion, and it is a convenient reference point for many other calculations in physics, such as angular momentum or themoment of inertia. In many applications, such as orbital mechanics, objects can be replaced by point masses located at their mass centers for the purposes of analysis. The center of mass frame is aninertial frame in which the center of mass of a system is at rest at the origin of the coordinate system.
In a uniform gravitational field, such as for small bodies near the surface of Earth, the weight of a body acts as if it were concentrated at the center of mass. For this reason, the center of mass is also called the center of gravity. Where gravity is not uniform, there can be a gravitational torque acting on objects. In some situations, this torque can be explained as arising from a generalized center of gravity that is distinct from the center of mass.

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