Question
Download Solution PDFA sphere rolls down an inclined plane without slipping. What fraction of its total energy is rotational ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
A sphere rolling without slipping has both translational and rotational kinetic energy.
Rotational Kinetic Energy (KR) = (1/2) × I × (v2 / r2)
Moment of Inertia of a solid sphere, I = (2/5)mr2
So, KR = (1/2) × (2/5)mr2 × (v2 / r2) = (1/5)mv2
Translational Kinetic Energy (KTr) = (1/2)mv2
Total Energy (KTotal) = KR + KTr = (1/5)mv2 + (1/2)mv2
Convert to common denominator:
KTotal = (2/10 + 5/10)mv2 = (7/10)mv2
Fraction of Rotational Energy = KR / KTotal = (1/5)mv2 / (7/10)mv2
Cancel mv2:
Fraction = (1/5) / (7/10) = (2/7)
Answer: Option 1) 2/7
Last updated on Jun 6, 2025
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