Is this question correct or else what should be the correct way of asking the following question?
Find the position of centre of gravity of a cone of height h and base radius r
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This is not properly formed because of three reasons,
1) Shape of the object should be precisely stated, it should be given as right circular cone instead of just a cone.
2)Distribution of particles within the object should be mentioned, it should be given as uniform otherwise density need to be given as a function.
3)Without knowing the numerical values of dimensions we can not assume centre of mass is at the same position of centre of gravity. Therefore the correct way is to ask position of centre of mass.