Question

How many drops of water are in a 1.0 L bottle? (Hint: Start by estimating the diameter of a drop of water.)

Answer 1

Answer:

N = 2000 drops approx with 1 cm diameter each

Explanation:

Let the diameter of one drop is 1 cm

so volume of one drop is given by

$V = \frac{1}{6}\pi d^3$

now we have

$V = \frac{1}{6}\pi(0.01)^3$

$V = 0.53 \times 10^{-6} m^3$

now in 1L of liquid let say N drops are there

so we have

$1L = 10^{-3} m^3$

now we have

$N = \frac{10^{-3}}{0.53 \times 10^{-6}}$

$N = 2\times 10^3$

so it will have approx 2000 drops in it with diameter 1 cm each drop

Answer 2

The number of drops in water bottle  

Further Explanation:

The number of droplets present in one water bottle is given as the ratio of the total volume contained in the bottle to the volume of one droplet of the water present inside the bottle.

Consider that the diameter of one drop of water is $2\,{\text{mm}}$.

Write the expression for the volume of one drop of water.

$V = \dfrac{4}{3}\pi {\left( {\dfrac{d}{2}} \right)^3}$    …… (I)                                                                                                    

Substitute the value of $d$ in above expression.

$\begin{aligned}V&= \frac{4}{3}\pi \left( {\frac{{2 \times {{10}^{ - 3}}\,{\text{m}}}}{2}} \right)\\&= 4.188 \times {10^{ - 9}}\,{{\text{m}}^{\text{3}}}\\\end{aligned}$  

Convert the volume of one litre to ${m^3}$.

$1\,l = {10^{ - 3}}\,{m^3}$

Therefore, the number of water droplets present in $1\,l$ of water is.

$\begin{aligned}n&= \frac{{{{10}^{ - 3}}\,{{\text{m}}^{\text{3}}}}}{{4.188 \times {{10}^{ - 9}}\,{{\text{m}}^{\text{3}}}}}\\&= 2.38 \times {10^5}\,{\text{droplets}} \\ \end{aligned}$  

Thus, the number of droplets present in the bottle of one litre water is $\boxed{2.38 \times {{10}^5}}$ droplets.

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Answer Details:

Grade: College

Chapter: Units and Measurement

Subject: Physics

Keywords: Drops of water, 1.0L water, bottle, diameter of drop, volume of drop, number of droplets, in bottle.