Question

The moment of inertia of a disc about its geometrical axis is $I$. then its moment of inertia about its diameter will be

• A. $I$
  
• B. $2I$
  
• C. $\frac{I}{2}$
  
• D. $\frac{I}{4}$
  

Answer 1

The correct option is C $\frac{I}{2}$

$I_z=I$(given)

$I_z=I_x+I_y$(axis theorem)

$I_x=I_y$(By symmetry)

$\therefore I_x=I_y=\frac{I}{2}$

$\therefore$ MOI about diameter is $\frac{I}{2}$