JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion

Suppose there is a uniform circular disc of mass M kg and radius r m shown in figure. The shaded regions are cut out from the disc. The moment of inertia of the remainder about the axis A of the disc is given by \(\frac{ x }{256} Mr ^2\). The value of x is ___________.

A 100
B 109
C 128
D 156

Verified Solution

Answer & Solution

Correct Answer

(B) 109

Step-by-step Solution

Detailed explanation

\(M =\sigma \pi R ^2\) \(\sigma \pi R ^2=16 m\) \(m =\frac{\sigma \pi R ^2}{16}\) \(I _{\text {system }}=\frac{ MR ^2}{2}-2\left(\frac{ mR ^2}{2 \times 16}+\frac{9 mR ^2}{16}\right)\) \(=\frac{ MR ^2}{2}-2 \times \frac{19 mR ^2}{32}\) \(=\frac{ MR ^2}{2}-\frac{19}{16} mR ^2\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match List - I with List - II.

List-I	List-II
(A) Angular Impulse	(I) \(\left[M^0 L^2 T^{-2}\right]\)
(B) Latent Heat	(II) \(\left[M L^2 T^{-3} A^{-1}\right]\)
(C) Electrical resistivity	(III) \(\left[M L^2 T^{-1}\right]\)
(D) Electromotive force	(IV) \(\left[M L^3 T^{-3} A^{-2}\right]\)

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