A) \[\frac{{{m}_{2}}{{d}_{2}}-{{m}_{1}}{{d}_{1}}}{{{m}_{2}}-{{m}_{1}}}\]
B) \[\frac{{{m}_{1}}{{d}_{1}}-{{m}_{2}}{{d}_{2}}}{{{m}_{2}}-{{m}_{1}}}\]
C) \[\frac{{{m}_{2}}{{d}_{1}}-{{m}_{1}}{{d}_{2}}}{{{m}_{1}}-{{m}_{2}}}\]
D) \[\frac{{{m}_{1}}{{d}_{2}}-{{m}_{2}}{{d}_{1}}}{{{m}_{1}}-{{m}_{2}}}\]
Correct Answer: D
Solution :
Given that an object weighs \[{{m}_{1}}\]in a liquid of density \[{{d}_{1}}\]and \[{{m}_{2}}\] in a liquid of density\[{{d}_{2}},\] so when the density of the object is d, then we get \[V(d-{{d}_{1}})={{m}_{1}}\] And \[V(d-{{d}_{2}})={{m}_{2}}\] Thus, \[\frac{d-{{d}_{1}}}{d-{{d}_{2}}}=\frac{{{m}_{1}}}{{{m}_{2}}}\] So, we get \[\frac{{{m}_{1}}{{d}_{2}}-{{m}_{2}}{{d}_{1}}}{{{m}_{1}}-{{m}_{2}}}.\]
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