Question

For the body shown in the figure:


Statement $1:I_z=I_x+I_y$
Statement $2:I_x=I_z+I_y$ and $I_y=I_x+I_z$
where $x$, $y$ and $z$ are the axes of rotation of the body.
Choose the correct option.

• A. $\text{Statement}2\text{is correct and statement}1\text{is incorrect.}$
• B. $\text{Statement}1\text{is correct and statement}2\text{is incorrect.}$
• C. $\text{Both statements are correct}$
• D. $\text{None of these}$

Answer 1

The correct option is B $\text{Statement}1\text{is correct and statement}2\text{is incorrect.}$


Using Perpendicular axes theorem,
$I_z=I_x+I_y$

But $I_x=I_z+I_y$ is incorrect as $z$ and $y$ are not in the plane of the body.
Similarly,
$I_y=I_x+I_z$ is incorrect as $x$ and $z$ are not in the plane of the body.
$\therefore$ Statement $1$ is correct and statement $2$ is incorrect.