Properties Of Solids And Liquids Question 287
Question: A body of density $ d _{1} $ is counterpoised by $ Mg $ of weights of density $ d _{2} $ in air of density d. Then the true mass of the body is
Options:
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})} $
Show Answer
Answer:
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]} $
