Answer:
Density of Sand is [tex]2.653g/cm^{3}[/tex].
Explanation:
Given Empty Density bottle weighs 23.5gm(W=23.5gm)
Weight of bottle when completely filled water=48.4gm
So amount of water required to fill the bottle=Weight of bottle filled with water-W
Amount of water required to fill the bottle([tex]w_{max}[/tex])=48.4gm-23.5gm
[tex]w_{max}=24.9[/tex]g
Since we know density of water [tex]d_{w} =1g/cm^{3}[/tex] and [tex]w_{max}[/tex]
We can calculate volume of empty space in the bottle(V).
[tex]w_{max}=d_{w}[/tex][tex]\times[/tex]V
V=[tex]\frac{w_{max} }{d_{w} }[/tex]
V=[tex]\frac{24.9}{1}[/tex]
V=24.9 [tex]g/cm^{3}[/tex]
Now bottle is partially filled with sand,and weight of bottle is ([tex]w_{s}[/tex])36.5gm
So,
Amount of sand added ([tex]m_{s}[/tex])=36.5-Weight of the bottle
[tex]m_{s}[/tex]=13g
After filling the bottle with water again,the weight of the bottle becomes ([tex]W_{2}[/tex]=56.5g)
Therefore,
amount of water added to the bottle of sand in grams = [tex]W_{2}[/tex]-36.5gm
amount of water added =56.5g-36.5g
amount of water added =20g
As the density of water = 1g/[tex]cm^{3}[/tex]
Amount of water (in grams )=Volume of water occupied
20=volume of water added
Therfore volume of water added to the sand filled bottle([tex]V_{w}[/tex])=20[tex]cm^{3}[/tex]
As we know the total volume of the water bottle(V),
Volume of the sand occupied in the water bottle=V-[tex]V_{w}[/tex]
[tex]V_{s}[/tex]=24.9g-20g
[tex]V_{s}[/tex]=4.9g
We know,
Density=Mass/Volume
Therefore,
density of sand = [tex]\frac{m_{s} }{V_{s} }[/tex]
density of sand =[tex]\frac{13}{4.9}[/tex]
density of sand = [tex]2.653g/cm^{3}[/tex]
