First slide

Moment of intertia

Question

A thin uniform circular ring of mass M and radius R is in XY plane with its center coinciding with the origin. If it’s moment of inertia about Z-axis is same as its moment of inertia about the line y = x + c, the value of c is

Difficult

A

$\sqrt{2} R$
B

R
C

$\frac{R}{2}$
D

$\frac{R}{\sqrt{2}}$

Solution

$m o m e n t o f i n e r t i a a b o u t Z a x i s = M R^{2} m o m e n t o f i n e r t i a a b o u t a d i a m e t e r p a r a l l e l t o t h e l i n e = \frac{M R^{2}}{2} y = x + c s l o p e o f t h e l i n e i s 1 i . e, θ = 45^{0} p e r p e n d i c u l a r d i s \tan c e b e t w e e n t h e l i n e s = c \sin 45^{0} a p p l y i n g p a r a l l e l a x i s t h e o r e m M R^{2} = \frac{M R^{2}}{2} + M {(c \sin 45^{0})}^{2} s o l v i n g c = R$

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