એક સમાન \(6\, kg\) દળ ધરાવતાં અને \(2.4\, meter\) લંબાઈ ધરાવતાં પાતળા પટ્ટાને વાળીને એક સમતુલ્ય ષષ્ટકોણ બનાવવામાં આવે છે. ષષ્ટકોણનાં સમતલને લંબ અને દ્રવ્યમાન કેન્દ્રમાંથી પસાર થતી અક્ષને અનુલક્ષીને જડત્વની ચાકમાત્રા ...... \(\times \,10^{-1} \,kg m ^{2}\) હશે.

A \(16\)
B \(8\)
C \(24\)
D \(4\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(8\)

Step-by-step Solution

Detailed explanation

\(6 \ell=2.4 \quad \ell=0.4 \,m\) \(\sin 60^{\circ}=\frac{ r }{\ell}\) \(r =\ell \sin 60^{\circ}=\frac{\ell \sqrt{3}}{2}\) MOI, \(\quad I=\left[\frac{m \ell^{2}}{12}+\operatorname{mr}^{2}\right] 6\)…

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.

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