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L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator sin begin display style space end style a x over denominator x cos space x end fraction

Maths-General

  1. 1
  2. 0
  3. none of these

  4. a

    Answer:The correct answer is: a

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    T subscript 1 end subscript cos invisible function application 30 degree plus T subscript 2 end subscript cos invisible function application 45 degree equals m g(i)
    T subscript 1 end subscript sin invisible function application 30 degree plus T subscript 2 end subscript sin invisible function application 45 degree equals fraction numerator m v to the power of 2 end exponent over denominator r end fraction (ii)
    After solving Eq. (i) and eq. (ii), we get
    T subscript 1 end subscript equals fraction numerator m g minus fraction numerator m v to the power of 2 end exponent over denominator r end fraction over denominator open parentheses fraction numerator square root of 3 minus 1 over denominator 2 end fraction close parentheses end fraction
    But T subscript 1 end subscript greater than 0
    therefore fraction numerator m g minus fraction numerator m v to the power of 2 end exponent over denominator r end fraction over denominator fraction numerator square root of 3 minus 1 over denominator 2 end fraction end fraction greater than 0

    or m g greater than fraction numerator m v to the power of 2 end exponent over denominator r end fraction
    or v less than square root of r g end root
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    From force diagram shown in figure
    T subscript 1 end subscript cos invisible function application 30 degree plus T subscript 2 end subscript cos invisible function application 45 degree equals m g(i)
    T subscript 1 end subscript sin invisible function application 30 degree plus T subscript 2 end subscript sin invisible function application 45 degree equals fraction numerator m v to the power of 2 end exponent over denominator r end fraction (ii)
    After solving Eq. (i) and eq. (ii), we get
    T subscript 1 end subscript equals fraction numerator m g minus fraction numerator m v to the power of 2 end exponent over denominator r end fraction over denominator open parentheses fraction numerator square root of 3 minus 1 over denominator 2 end fraction close parentheses end fraction
    But T subscript 1 end subscript greater than 0
    therefore fraction numerator m g minus fraction numerator m v to the power of 2 end exponent over denominator r end fraction over denominator fraction numerator square root of 3 minus 1 over denominator 2 end fraction end fraction greater than 0

    or m g greater than fraction numerator m v to the power of 2 end exponent over denominator r end fraction
    or v less than square root of r g end root
    therefore blank v subscript m a x end subscript equals square root of r g end root equals square root of 1.6 cross times 9.8 end root equals 3.96 blank m s to the power of negative 1 end exponent
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