Question

A body having its centre of mass at the origin has three of its particles at $(a,0,0),(0,a,0),(0,0,a)$ the moment of inertia of the body about $X$ and $Y$ axis are $0.2kg{m}^2$ the moment of inertia about its $Z$ axis is

• A. is $0.20kg-m^2$
• B. is $0.40kg-m^2$
• C. $0.20\sqrt{2}kg-m^2$
• D. cannot be deducted with this information

Answer 1

The correct option is D cannot be deducted with this information

Given,

the moment of inertia of the body about X and Y axis are $0.2kg{m}^2$

ie $I_X=m_2{a}^2+m_3{a}^2=0.2$

and, $I_Y=m_1{a}^2+m_3{a}^2=0.2$

and C.O.M is at origin.

And we have yo find ;

$I_Z=m_1{a}^2+m_2{a}^2=?$

here ,

we have 2 equation and 3-variable $(m_1,m_2,m_3)$

hence,

$I_Z$ cannot be deducted with this information.