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Easy

Question

Find the velocity of centre of the system shown in the figure.

  1. open parentheses fraction numerator 2 plus 2 square root of 3 over denominator 3 end fraction close parentheses stack i with hat on top minus fraction numerator 2 over denominator 3 end fraction stack j with hat on top    
  2. 4stack i with hat on top    
  3. open parentheses fraction numerator 2 minus 2 square root of 3 over denominator 3 end fraction close parentheses stack i with hat on top minus fraction numerator 1 over denominator 3 end fraction stack j with hat on top    
  4. None of these    

The correct answer is: open parentheses fraction numerator 2 plus 2 square root of 3 over denominator 3 end fraction close parentheses stack i with hat on top minus fraction numerator 2 over denominator 3 end fraction stack j with hat on top


    Here, m subscript 1 end subscript equals 1 kg, stack v with rightwards arrow on top subscript 1 end subscript equals 2 stack i with hat on top
    m subscript 2 end subscript equals 2 kg, stack v with rightwards arrow on top subscript 2 end subscript equals 2 cos invisible function application 30 stack i with hat on top minus 2 sin invisible function application 30 stack j with hat on top
    stack v with rightwards arrow on top subscript C M end subscript equals fraction numerator m subscript 1 end subscript stack v with rightwards arrow on top subscript 1 end subscript plus m subscript 2 end subscript stack v with rightwards arrow on top subscript 2 end subscript over denominator m subscript 1 end subscript plus m subscript 2 end subscript end fraction
    equals fraction numerator 1 cross times 2 stack i with hat on top plus 2 left parenthesis 2 cos invisible function application 30 degree stack i with hat on top minus 2 sin invisible function application 30 degree stack j with hat on top right parenthesis over denominator 1 plus 2 end fraction
    equals fraction numerator 2 stack i with hat on top plus 2 square root of 3 stack i with hat on top minus 2 stack j with hat on top over denominator 3 end fraction equals open parentheses fraction numerator 2 plus 2 square root of 3 over denominator 3 end fraction close parentheses stack i with hat on top minus fraction numerator 2 over denominator 3 end fraction stack j with hat on top

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