AP EAMCET202023 Sep 2020Morning ShiftChemistryp Block Elements (Group 13 & 14)Actual
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
Options
- AK 2 + R 2 K 2
- BK 2 R 2
- CK 2 K 2 + R 2
- DR 2 K 2 + R 2
Correct answer
C. K 2 K 2 + R 2
Step-by-step solution
in pure rolling motion Rotational KE K R = 1 2 m K 2 ω 2 = 1 2 m v 2 K 2 R 2 Total KE K E = 1 2 m v 2 1 + K 2 R so K R K E = 1 2 m v 2 K 2 R 2 1 2 m v 2 1 + K 2 R 2 = K 2 K 2 + R 2