આકૃતિમાં દર્શાવ્યા મુજબ \(M\) દળ અને \(R\) ત્રિજ્યાની એક પાતળી નિયમિત તકતીમાં \(\frac{R}{4}\) ત્રિજ્યાનો વર્તુળાકાર છેદ પાડેલો છે. તો બાકી રહેલા ભાગ ની તેના \(O\) માથી પસાર થતી અક્ષને અનુલક્ષીને તકતીના સમતલને લંબ જડત્વની ચાકમાત્રા શું થાય?

A \(\frac{{219\,M{R^2}}}{{256}}\)
B \(\frac{{237\,M{R^2}}}{{512}}\)
C \(\frac{{19\,M{R^2}}}{{512}}\)
D \(\frac{{197\,M{R^2}}}{{256}}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{{237\,M{R^2}}}{{512}}\)

Step-by-step Solution

Detailed explanation

Moment of Inertia of complete disc about \('O'\) point \({I_{total}} = \frac{{M{R^2}}}{2}\) Radius of removed disc \(= R/4\) Mass of removed disc \(= M/16\) [As \(M\) \( \propto \) \({{R^2}}\)] \(M.I.\) of removed disc about its own axis \((O')\)…

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

Explore more questions on app

From JEE Mains

Explore more questions on app