A uniform disc of radius `R` lies in the `x-y` plane, with its centre at origin. Its moment of inertia about z-axis is equal to its moment of inertia about line `y = x + c`. The value of `c` will be.
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Options

A. ` - (R )/(2)`
B. `+- ( R)/(sqrt(2))`
C. `(+ R)/(4)`
D. ` - R`

Answer

B

Explanation

(b) `I_(PQR) = I_(AOB) + M.(ON)^2 I_(PQR) = (1)/(4) MR^2 + M.(c/(sqrt(2)))^(2)`
But `I_(PQR) = (1)/(2) MR^2` :. `c = +- ( R)/(sqrt(2))`
Hence (b) is correct.
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