The correct option is (b) 3h/4.
Explanation:
Suppose the cylindrical symmetry of the problem to note that the center of mass must lie along the z axis (x = y = 0). The only issue is how high does it lie. If the uniform density of the cone is ρ , then first compute the mass of the cone. If we slice the cone into circular disks of area πr2 and height dz, the mass is given by the integral:
However, we know that the radius r starts at a for z = 0, and goes linearly to zero when z = h . This means that, r = a (1-z/h), so that:
As a result, the center of mass of the cone is along the symmetry axis, one quarter of the way up from the base to the tip and 3/4 h from the tip.