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A dumbbell is placed in water of density rho. It is observed that by attaching a mass m to the rod, the dumbbell floats with the rod horizontal on the surface of water and each sphere exactly half submerged as shown in the figure. The volume of the mass m is negligible. The value of length l is

  1. fraction numerator d open parentheses V subscript rho end subscript minus 3 M close parentheses over denominator 2 open parentheses V subscript rho end subscript minus 2 M close parentheses end fraction    
  2. fraction numerator d open parentheses V subscript rho end subscript minus 2 M close parentheses over denominator 2 open parentheses V subscript rho end subscript minus 3 M close parentheses end fraction    
  3. fraction numerator d open parentheses V subscript rho end subscript plus 2 M close parentheses over denominator 2 open parentheses V subscript rho end subscript minus 3 M close parentheses end fraction    
  4. fraction numerator d open parentheses V subscript rho end subscript minus 2 M close parentheses over denominator 2 open parentheses V subscript rho end subscript plus 3 M close parentheses end fraction    

The correct answer is: fraction numerator d open parentheses V subscript rho end subscript minus 2 M close parentheses over denominator 2 open parentheses V subscript rho end subscript minus 3 M close parentheses end fraction

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