AP EAMCET · Chemistry · p Block Elements (Group 13 & 14)

A uniform solid sphere of radius $R$ and radius of gyration $K$ about an axis passing through the centre of mass, is rolling without slipping. Then the fraction of total energy associated with its rotation will be

A $\frac{K^{2} + R^{2}}{K^{2}}$
B $\frac{K^{2}}{R^{2}}$
C $\frac{K^{2}}{K^{2} + R^{2}}$
D $\frac{R^{2}}{K^{2} + R^{2}}$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{K^{2}}{K^{2} + R^{2}}$

Step-by-step Solution

Detailed explanation

in pure rolling motion Rotational KE KR=12mK2ω2=12mv2K2R2 Total KE KE=12mv21+K2R so KRKE=12mv2K2R212mv21+K2R2=K2K2+R2

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 AP EAMCET

Explore more questions on app

A uniform solid sphere of radius R and radius of gyration K about an axis passing through the centre of mass, is rolling without slipping. Then the fraction of total energy associated with its rotation will be

Step-by-step Solution

A uniform solid sphere of radius $R$ and radius of gyration $K$ about an axis passing through the centre of mass, is rolling without slipping. Then the fraction of total energy associated with its rotation will be