બે સમાન ધન ગોળાઆ કે દરેકનું વજન \(2\,kg\) અને ત્રિજ્યા \(10\,cm\) છે તેને હળવા સળિયાના છેડા પર લગાડવામાં આવે છે. ગોળાના કેન્દ્રો વચ્યેનું અંતર \(40\,cm\) છે. સળીયાની અક્ષને લંબરૂપે તેના મધ્ય બિંદ્દુને અનુલક્ષીને તંત્રની જડત્વની ચાકમાત્રા \(........\times 10^{-3}\,kg - m ^2\) છે.

A \(177\)
B \(178\)
C \(198\)
D \(176\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(176\)

Step-by-step Solution

Detailed explanation

\(I =2\left( I _{ cm }+ md ^2\right)\) \(=2\left(\frac{2}{5} mr ^2+ md ^2\right)\) \(=\frac{4}{5} \times 2 \times(0.1)^2+2(2)(0.20)^2\) \(=\frac{8}{5} \times 10^{-2}+16 \times 10^{-2}\) \(=(1.6+16) \times 10^{-2}\) \(=17.6 \times 10^{-2}\) \(I =176 \times 10^{-3}\,kg\,m ^2\)

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.

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