\(80\, {cm}\) લંબાઈ અને \({M}\) દળ ધરાવતા ઘન નળાકારની ત્રિજ્યા \(20\, {cm}\) છે. આકૃતિમાં દર્શાવેલ \(AB\) ને સમાંતર \(CD\) અક્ષને અનુલક્ષીને જડત્વની ચાકમાત્રા \(2.7\, {kg} {m}^{2}\) હોય તો પદાર્થની ઘનતાની (\({kg} / {m}^{3}\) માં) ગણતરી કરો.

A \(14.9\)
B \(75\)
C \(750\)
D \(149\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(149\)

Step-by-step Solution

Detailed explanation

Parallel axis theorem \({I}={I}_{{CM}}+{Md}^{2}\) \({I}=\frac{{Mr}^{2}}{2}+{M}\left(\frac{{L}}{2}\right)^{2}\) \(2.7={M} \frac{(0.2)^{2}}{2}+{M}\left(\frac{0.8}{2}\right)^{2}\) \(2.7={M}\left[\frac{2}{100}+\frac{16}{100}\right]\) \({M}=15\, {kg}\)…

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

સૂચિ - I	સૂચિ - II
(A) સમદાબ	(I) ΔQ = ΔW
(B) સમકદ	(II) ΔQ = ΔU
(C) સમમોષ્મી	(III) ΔQ = zero
(D) સમતાપી	(IV) ΔQ = ΔU + PΔV

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