Find centre of mass of an object (Paraboloid) which is formed by rotating a parabola `x=ky^(2)` about x-axis and height of object is h as shown in figure. Assume the object is of uniform density.

The centre of a mass of any object having uniform density is at its centroid

Find out the centre of mass of a composite object shown in figure. Object consists of a cone with its base joint with the base of a hemisphere. The dimensions of the object are shown in figure. Assume uniform density of the system.

Three particles, each of mass m are placed an the points (x_(1),y_(1),z_(1)),(x_(2),y_(2),z_(2)) and (x_(3),y_(3),z_(3)) on the inner surface of a paraboloid of revolution obtained by rotating the parabola x^(2)=4ay about the y -axis. Neglected the mass of the paraboloid. ( y -axis. is along the vertical (a) the moment of inertia of the system about the axis of the paraboloid is I=4ma(y_(1)+y_(2)+y_(3))

From a hemisphere of radius R a cone of base radius R/w and height R is cut as shown in figure. Find the height of centre of mass of the remaining object.

The y co - ordinate of the centre of mass of the system of three rods of length 2a and two rods of length a as shown in the figure is (Assume all rods to be of uniform density)