Question

The density of liquid in which hydrometer sinks to the top of stem is X $gc{m}^{-3}$. Find [10X]. {Where , [] is a step function}

• A. 0.9
• B. 9
• C. 90
• D. 900

Answer 1

The correct option is B 9

Let the volume of hydrometer bulb be $V$.
When hydrometer sinks to the mark 5 cm of the stem.
Using the law of flotation, we have
$(V+5)\times D_w\times g=200\times g$
Because, $D_w=1g/{cm}^3$.
$V=1{95cm}^3$.
When the hydrometer sinks to the top,
$(195+10)\times D_L\times g=200\times g$.
$D_L=\frac{200}{205}=0.9g/{cm}^3$.
Hence, the density of liquid in which hydrometer sinks to the top of stem is $0.9g/{cm}^3$ = X and the answer 10X = 9.