question_answer

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)         \[\sqrt{{{w}_{1}}^{2}+{{w}^{2}}_{2}}\]

Correct Answer: B

Solution :

            \[(x+w)l=(y+{{w}_{1}})l\] \[\therefore \]      \[x+w=y+{{w}_{1}}\]                          ? (i) and       \[x+{{w}_{2}}=y+w\]                          ? (ii) Substracting equation (ii) from (i), we get \[\therefore \]      \[w-{{w}_{2}}={{w}_{1}}-w\] \[\Rightarrow \]   \[w=\frac{1}{2}({{w}_{1}}+{{w}_{2}})\]