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A hollow sphere of mass M and radius r is immersed in a tank of water text (density  end text rho subscript w end subscript text  ). end text The sphere would float if it were set free. The sphere is tied to the bottom of the tank by two wires which makes angle 45° with the horizontal as shown in the figure. The tension T subscript 1 end subscript in the wire is :

  1. fraction numerator fraction numerator 4 over denominator 3 end fraction pi R to the power of 3 end exponent rho subscript w end subscript g minus M g over denominator square root of 2 end fraction    
  2. fraction numerator 2 over denominator 3 end fraction pi R to the power of 3 end exponent rho subscript w end subscript g minus M g    
  3. fraction numerator fraction numerator 4 over denominator 3 end fraction pi R to the power of 3 end exponent rho subscript w end subscript g minus M g over denominator 2 end fraction    
  4. fraction numerator 4 over denominator 3 end fraction pi R to the power of 3 end exponent rho subscript w end subscript g plus M g    

The correct answer is: fraction numerator fraction numerator 4 over denominator 3 end fraction pi R to the power of 3 end exponent rho subscript w end subscript g minus M g over denominator square root of 2 end fraction

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