Physics-
General
Easy

Question

A spherical ball rolls on a table without slipping. Then the fraction of its total energy associated with rotation is -

  1. 2/5  
  2. 2/7  
  3. 3/5  
  4. 3/7  

The correct answer is: 2/7


    Total energy
    K = KR + KT = fraction numerator 1 over denominator 2 end fraction I2 + fraction numerator 1 over denominator 2 end fractionmv2
    = fraction numerator 1 over denominator 2 end fraction open parentheses fraction numerator 2 over denominator 5 end fraction m r to the power of 2 end exponent close parentheses2 + fraction numerator 1 over denominator 2 end fraction mr22
    = fraction numerator 1 over denominator 5 end fractionmr22 + fraction numerator 1 over denominator 2 end fraction mr2 2 = fraction numerator 7 over denominator 10 end fraction mr22
    Now, rotational kinetic energy
    KR = fraction numerator 1 over denominator 2 end fractionI2 = fraction numerator 1 over denominator 5 end fraction mr22
    fraction numerator K subscript R end subscript over denominator K end fraction = fraction numerator fraction numerator 1 over denominator 5 end fraction m r to the power of 2 end exponent omega to the power of 2 end exponent over denominator fraction numerator 7 over denominator 10 end fraction m r to the power of 2 end exponent omega to the power of 2 end exponent end fraction = fraction numerator 2 over denominator 7 end fraction

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