Physics-
General
Easy

Question

A particle P is moving on a circle under the action of only one force acting always towards fixed point O on the circumference . The ratio of fraction numerator d to the power of 2 end exponent theta over denominator d t to the power of 2 end exponent end fraction and open parentheses fraction numerator d theta over denominator d t end fraction close parentheses to the power of 2 end exponent

  1. fraction numerator tan invisible function application theta over denominator 2 end fraction    
  2. 4 tantheta    
  3. tantheta    
  4. 2 tantheta    

The correct answer is: 2 tantheta


    fraction numerator d left parenthesis 2 theta right parenthesis over denominator d t end fraction equals omega

    centripetal force = Fcosq = mw2r rightwards double arrow omega equals square root of fraction numerator F c o s invisible function application theta over denominator m r end fraction end root
    2 fraction numerator d theta over denominator d t end fraction equals square root of fraction numerator F c o s invisible function application theta over denominator m r end fraction end root rightwards double arrow fraction numerator d theta over denominator d t end fraction equals fraction numerator 1 over denominator 2 end fraction square root of fraction numerator F c o s invisible function application theta over denominator m r end fraction end root
    Þ tangential force = Fsinq
    alpha r equals fraction numerator F s i n invisible function application theta over denominator m end fraction
    fraction numerator d to the power of 2 end exponent open parentheses 2 theta close parentheses over denominator d t to the power of 2 end exponent end fraction equals fraction numerator F s i n invisible function application theta over denominator m r end fraction
    fraction numerator d to the power of 2 end exponent left parenthesis theta right parenthesis over denominator d t to the power of 2 end exponent end fraction equals fraction numerator F s i n invisible function application theta over denominator 2 m r end fraction
    Ratio fraction numerator d to the power of 2 end exponent theta over denominator d t to the power of 2 end exponent end fraction open parentheses fraction numerator d theta over denominator d t end fraction close parentheses to the power of 2 end exponent equals fraction numerator F s i n invisible function application theta over denominator 2 m r end fraction divided by fraction numerator 1 over denominator 4 end fraction fraction numerator F c o s invisible function application theta over denominator m r end fraction equals 2 t a n invisible function application theta

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