A) M
B) \[M\,\left( 1-\frac{d}{{{d}_{2}}} \right)\]
C) \[M\left( 1-\frac{d}{{{d}_{1}}} \right)\]
D) \[\frac{M(1-d/{{d}_{2}})}{(1-d/{{d}_{1}})}\]
Correct Answer: D
Solution :
Let \[{{M}_{0}}=\]mass of body in vacuum. Apparent weight of the body in air = Apparent weight of standard weights in air \[\Rightarrow \] Actual weight ? upthrust due to displaced air = Actual weight ? upthrust due to displaced air \[\Rightarrow \]\[{{M}_{0}}g-\left( \frac{{{M}_{0}}}{{{d}_{1}}} \right)\,dg=Mg-\left( \frac{M}{{{d}_{2}}} \right)\,dg\] \[\Rightarrow {{M}_{0}}=\frac{M\left[ 1-\frac{d}{{{d}_{2}}} \right]}{\left[ 1-\frac{d}{{{d}_{1}}} \right]}\]
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