Question

The diagram shows a uniform solid cone of height h and mass M. If the moment of the cone about$XY$ is $1,$ its moment of inertia about $PQ$ is

• A. I $M{h}^2$
• B. ${Mh}^2-I$
• C. $I+\frac{1}{2}M{h}^2$
• D. $I-\frac{1}{2}{Mh}^2$

Answer 1

Answer: (B)

${Mh}^2-I$

$\begin{array}{c}\text{given- moment of Inertia about axis}xY=I\\ \text{Let the moment of Inertia about axis}Q\text{p be}{I}^{\prime }\\ \Rightarrow \text{Moment of Inertia about}xY\text{can be given as}\\ \text{By parallel}ax\text{is theorem-}\\ \begin{array}{c}I=I^{\prime }+M{h}^2\\ \Rightarrow I^{\prime }=M{h}^2-I\end{array}\end{array}$