Question

A particle of mass $m$ is located at point O. Find $I_A,I_B,I_{AB}$ and $I_{A{A}^{\prime }}$ respectively.

• A. $m{d}^2,m{d}^2{\tan }^2\theta ,m{d}^2,m{d}^2{\sin }^2\theta$
• B. $m{d}^2,m{d}^2{\tan }^2\theta ,m{d}^2{\sin }^2\theta ,m{d}^2$
• C. $0,m{d}^2{\tan }^2\theta ,m{d}^2,0$
• D. $m{d}^2\sin \theta ,0,m{d}^2,0$

Answer 1

The correct option is B $m{d}^2,m{d}^2{\tan }^2\theta ,m{d}^2{\sin }^2\theta ,m{d}^2$


From above figure
$y=d\tan \theta ;x=d\sin \theta$

We know that,
$I=m{r_{\perp }}^2$
$r_{\perp }\text{is}\perp$ distance between the mass and axis of rotation.
$I_A=m(d{)}^2=m{d}^2$
$I_B=m{y}^2=m{d}^2{\tan }^2\theta$
$I_{AB}=m{x}^2=m{d}^2{\sin }^2\theta$
$I_{A{A}^1}=m{d}^2$