બે તકતી તેની અક્ષને અનુલક્ષીને સમાન દિશામાં ભ્રમણ કરે છે.પ્રથમ તકતીની જડત્વની ચાક્માત્રા \(0.1 \;kg \cdot m ^{2}\) અને કોણીય ઝડપ \(10\; rad \,s^{-1}\) છે,બીજી તકતીની જડત્વની ચાક્માત્રા \(0.2 \;kg - m ^{2}\) અને કોણીય ઝડપ \(5\; rad \,s ^{-1}\) છે,તેમની અક્ષને જોડીને એક તકતી બનાવતા તંત્રની ગતિઊર્જા ...........\(J\)

A \(3.33\)
B \(0.67\)
C \(1.67\)
D \(6.67\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(6.67\)

Step-by-step Solution

Detailed explanation

Both discs are rotating in same sense Angular momentum conserved for the system i.e. \(\quad L _{1}+ L _{2}= L _{\text {final }}\) \(I _{1} \omega_{1}+ I _{2} \omega_{2}=\left( I _{1}+ I _{2}\right) \omega_{ f }\) \(0.1 \times 10+0.2 \times 5=(0.1+0.2) \times \omega_{f}\)…

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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