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Question

A small mass particle is given an initial velocity v subscript 0 end subscript tangent to the horizontal rim of a smooth hemispherical bowl at radius r subscript 0 end subscript from the vertical centreline as shown at point A. As the particle slides past point B, on a vertical distance h below A and a distance r from the vertical centreline, its velocity v makes an angle theta with the horizontal tangentto the bowl through B.

  1. c o s invisible function application theta equals fraction numerator v subscript 0 end subscript r subscript 0 end subscript over denominator square root of v subscript 0 end subscript superscript 2 end superscript minus 2 g h end root square root of r subscript 0 end subscript superscript 2 end superscript minus h to the power of 2 end exponent end root end fraction    
  2. c o s invisible function application theta equals fraction numerator v subscript 0 end subscript r subscript 0 end subscript over denominator square root of v subscript 0 end subscript superscript 2 end superscript plus 2 g h end root square root of r subscript 0 end subscript superscript 2 end superscript plus h to the power of 2 end exponent end root end fraction    
  3. c o s invisible function application theta equals fraction numerator v subscript 0 end subscript r subscript 0 end subscript over denominator square root of v subscript 0 end subscript superscript 2 end superscript minus 2 g h end root square root of r subscript 0 end subscript superscript 2 end superscript plus h to the power of 2 end exponent end root end fraction    
  4. c o s invisible function application theta equals fraction numerator v subscript 0 end subscript r subscript 0 end subscript over denominator square root of v subscript 0 end subscript superscript 2 end superscript plus 2 g h end root square root of r subscript 0 end subscript superscript 2 end superscript minus h to the power of 2 end exponent end root end fraction    

The correct answer is: c o s invisible function application theta equals fraction numerator v subscript 0 end subscript r subscript 0 end subscript over denominator square root of v subscript 0 end subscript superscript 2 end superscript plus 2 g h end root square root of r subscript 0 end subscript superscript 2 end superscript minus h to the power of 2 end exponent end root end fraction

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