એક ફ્લાયવ્હીલની કોણીય ઝડપ 10 s માં 600 rpm થી 1200 rpm સુધી વધારવામાં આવે છે. આ સમય દરમિયાન ફ્લાયવ્હીલ દ્વારા પૂર્ણ થયેલા ભ્રમણની સંખ્યા છે :

A 900
B 600
C 150
D 300

Verified Solution

Answer & Solution

Correct Answer

(C) 150

Step-by-step Solution

Detailed explanation

(C) 150
પ્રારંભિક કોણીય ઝડપ, \(\omega_0=\frac{600 \times 2 \pi}{60}=20 \pi\ rad / s\)
અંતિમ કોણીય ઝડપ, \(\omega=\frac{1200 \times 2 \pi}{60}=40 \pi\ rad / s\)
કોણીય પ્રવેગ, \(\alpha=\frac{\omega-\omega_0}{t}=\frac{40 \pi-20 \pi}{10}=2 \pi\ rad / s ^2\)
કોણીય સ્થાનાંતર, \(\theta=\omega_0 t+\frac{1}{2} \alpha t^2\)
\(\theta=20 \pi \times 10+\frac{1}{2} \times 2 \pi \times(10)^2=200 \pi+100 \pi=300 \pi\ rad\)
ભ્રમણની સંખ્યા, \(N=\frac{\theta}{2 \pi}=\frac{300 \pi}{2 \pi}=150\)

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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