question_answer

Two cones A and B are made of two different materials, the density of A being greater than that of B. The height of B is greater than that of A but their base areas and masses are the same. The correct statement about the moment of inertia of the two cones about their axes, is

A)  A will have larger moment of inertia than B

B)  B will have larger moment of inertia than A

C)  in such a situation, it is dependent upon the height of the cone, the mass of the cone and radius of the base

D)  the moment of inertia of the two will be the same as it is not dependent upon height of the cone but depends only upon the mass and the base area

Correct Answer: B

Solution :

 Idea In this question one should understand that the moment of inertia of an rotating object depends on the mass distribution about the axis of rotation. \[{{h}_{A}}<{{h}_{B}}\] (heights) \[{{d}_{A}}>{{d}_{B}}\] (densities) B has larger shape and smaller density so, the same volume of B as volume of A will have smaller value of its mass due to increase density. So, the particles of B will be distributed far from the axis of rotation in comparison of A. So, \[{{l}_{B}}>{{l}_{A}}\] TEST Edge Questions where moment of inertia of a rotating object could be asked. These questions could be solved by integrating method or by the use of parallel and perpendicular axes theorems.