A false balance has equal arms. An object weights \[{{w}_{1}}\] when placed in one pan and \[{{w}_{2}}\] when placed in the other pan. Then weight w of the object is

• A.  \[\sqrt{{{w}_{1}}{{w}_{2}}}\]    
• B.         \[\frac{{{w}_{1}}+{{w}_{2}}}{2}\]  
• C.  \[\left( \frac{{{w}_{1}}^{2}+{{w}_{2}}^{2}}{2} \right)\]  
• D.         \[\sqrt{{{w}_{1}}^{2}+{{w}^{2}}_{2}}\]