Part CCSIR NET June 2024the-jacobian-adds-a-power-of-r

The jacobian adds a power of r

Consider a solid torus of constant density $ρ$ , formed by revolving the disc $(y - b)^{2} + z^{2} \leq a^{2}, x = 0$ about the z-axis, where 0 < a < b. Then the moment of inertia of the solid torus about the z-axis is

A. $2 π^{2} a^{2} b^{2} (4 b^{2} + 3 a^{2}) ρ$
B. $(π^{2} /2) a^{2} b (4 b^{2} + 3 a^{2}) ρ$ ✓
C. $(π^{2} /2) a^{2} b (4 a^{2} + 3 b^{2}) ρ$
D. $2 π^{2} a^{2} b^{2} (4 a^{2} + 3 b^{2}) ρ$

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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The jacobian adds a power of r

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