Question

A test tube of constant weight of length $10cm$ sinks to a depth $5cm$ in water. To the length will it sink in a liquid of relative density $1.25$, is $Xcm$. Find $X$.

• A. $1$
• B. $2$
• C. $4$
• D. $8$

Answer 1

Answer: (C)

$4$

The relative density of test tube when sinks up to depth of $5cm$ with respect to water is given as:

$V\times D_T\times g=\frac{1}{2}V\times D_w\times g$.
where,
$V$ = volume of the test tube
$D_T$ = density of the test tube
$D_w$ = density of water = $1g/{cm}^3$
So, $D_T=0.5g/{cm}^3$.
Now,
$V^{{}^{\prime }}\times D_L\times g=V\times D_T\times g$, where $D_L$ is the density of the liquid.
$⟹$ $\pi r^2{h}^{{}^{\prime }}\times D_L=\pi r^{2}h\times D_T$
$⟹$ $h^{{}^{\prime }}=h\times \frac{D_T}{D_L}=10\times \frac{0.5}{1.25}=4cm$.
Hence, the length it will sink in liquid of relative density 1.25 is 4 cm.