JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Rotational Mechanics

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The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is 'I(x)'. Which one of the graphs represents the variation of I(x) with x correctly?

(A)(see structure)
(B)(see structure)
(C)(see structure)
(D)(see structure)
✓ Correct

Answer: (D)

Solution

By the parallel-axis theorem the moment of inertia about an axis a distance

x

from the central diameter is

I (x) = I_{C M} + M x^{2} = \frac{2}{5} M R^{2} + M x^{2}

. This is an upward-opening parabola in

x

that does not pass through the origin but starts from the positive value

\frac{2}{5} M R^{2}

x = 0

. The graph that rises as a parabola from that non-zero intercept is the correct one.

JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Single correct option

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