Question

Spheres of iron and lead having the same mass are completely immersed in water. Density of lead is more than that of iron. Apparent loss of weight is $W_1$ for iron and $W_2$ for lead sphere. Then $\dfrac{{{W_1}}}{{{W_2}}}$ is
A. =1
B. Between 0 and 1
C. =0
D. >1

Answer 1

Hint: Apparent weight of the body is the weight which a body experiences when it travels through a fluid medium. The weight of the body measured inside a fluid is always different than the actual weight of the body.

Complete answer:
Since we know that the expression of relative density $RD$ is,
$RD = \dfrac{{actual\,weight}}{{loss\,of\,weight}}$
Since the actual weight of both iron and lead bodies are the same. Hence,
For the first body,
$
  R{D_1} = \dfrac{W}{{{W_1}}} \\
\Rightarrow {W_1} = \dfrac{W}{{R{D_1}}}......(I) \\
 $
Where $W$ is the actual weight of iron. and $W_1$ is the loss of weight for iron body. Similarly,
$
  R{D_2} = \dfrac{W}{{{W_2}}} \\
\Rightarrow {W_2} = \dfrac{W}{{R{D_2}}}......(II) \\
 $
Where $W$ is the actual weight of lead. and $W_2$ is the loss of weight for lead body
Therefore, divide equation (I) and equation (II).
$\Rightarrow \dfrac{{{W_1}}}{{{W_2}}} = \dfrac{{R{D_2}}}{{R{D_1}}}$
Since $R{D_2} > R{D_1}$.

Therefore, $\dfrac{{{W_1}}}{{{W_2}}} > 1$. So, option (D) is correct.

Additional information:
The loss of weight is due to the force of buoyancy which acts in a center of mass of the volume displaced by the body and it results in weightlessness. It entirely depends on the density of the fluid that is displaced by the body.

Note:
If the weight of the liquid displaced by the body is equal to the weight of the body then the object floats otherwise it sinks. After sinking then comes the concept of weightlessness. For example the speed of the ball dropped in the water slows down while it is moving inside the water.