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A small particle of mass m blankis projected at an angle theta with the x-axis with an initial velocity v subscript 0 end subscript in the x-y plane as shown in the figure. A t blank a blank t i m e blank t less than fraction numerator v subscript 0 end subscript sin invisible function application theta over denominator g end fraction comma the angular momentum of the particle is

  1. negative m g v subscript 0 end subscript t to the power of 2 end exponent cos invisible function application theta blank stack stack j with dot on top with hat on top    
  2. m g v subscript 0 end subscript t cos invisible function application theta blank stack k with hat on top    
  3. negative fraction numerator 1 over denominator 2 end fraction m g v subscript 0 end subscript t to the power of 2 end exponent cos invisible function application theta blank stack k with hat on top    
  4. fraction numerator 1 over denominator 2 end fraction m g v subscript 0 end subscript t to the power of 2 end exponent cos invisible function application theta blank stack stack i with dot on top with hat on top    

The correct answer is: negative fraction numerator 1 over denominator 2 end fraction m g v subscript 0 end subscript t to the power of 2 end exponent cos invisible function application theta blank stack k with hat on top


    L equals m open parentheses r cross times v close parentheses
    L equals m open square brackets v subscript 0 end subscript c o s theta blank t stack stack i with dot on top with hat on top plus open parentheses v subscript 0 end subscript s i n theta blank t minus fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent close parentheses stack stack j with dot on top with hat on top close square brackets
    cross times open square brackets v subscript 0 end subscript c o s theta blank stack stack i with dot on top with hat on top plus open parentheses v subscript 0 end subscript s i n theta minus g t close parentheses stack stack j with dot on top with hat on top close square brackets
    equals m v subscript 0 end subscript c o s theta blank t open square brackets negative fraction numerator 1 over denominator 2 end fraction g t close square brackets stack k with hat on top
    equals negative fraction numerator 1 over denominator 2 end fraction m g v subscript 0 end subscript t to the power of 2 end exponent c o s theta stack k with hat on top

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