Physics-
General
Easy

Question

A body of radius R and mass m is rolling horizontally without slipping with speed v. It then rolls up a hill to a maximum height h = fraction numerator 3 v to the power of 2 end exponent over denominator 4 g end fraction. The body might be a -

  1. solid sphere  
  2. hollow sphere  
  3. disc  
  4. ring  

The correct answer is: disc


    Let I bt the moment of inertia of the body. Then total KE = fraction numerator 1 over denominator 2 end fraction mv2 + fraction numerator 1 over denominator 2 end fractionI2
    or KE = fraction numerator 1 over denominator 2 end fractionmv2 + fraction numerator 1 over denominator 2 end fractionI fraction numerator v to the power of 2 end exponent over denominator R to the power of 2 end exponent end fraction open parentheses omega equals fraction numerator v over denominator R end fraction close parentheses
    According to energy conservation loss in KE = gain in PE.
    or open parentheses m plus fraction numerator I over denominator R to the power of 2 end exponent end fraction close parenthesesv2 = mgh = mgopen parentheses fraction numerator 3 v to the power of 2 end exponent over denominator 4 g end fraction close parentheses
    Solving this, we get I = fraction numerator 1 over denominator 2 end fractionmR2
    i.e., the solid body is a disc

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