Answer:
Density of Sand is
.
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(
)=48.4gm-23.5gm
g
Since we know density of water
and ![w_{max}](https://tex.z-dn.net/?f=w_%7Bmax%7D)
We can calculate volume of empty space in the bottle(V).
![w_{max}=d_{w}](https://tex.z-dn.net/?f=w_%7Bmax%7D%3Dd_%7Bw%7D)
V
V=![\frac{w_{max} }{d_{w} }](https://tex.z-dn.net/?f=%5Cfrac%7Bw_%7Bmax%7D%20%7D%7Bd_%7Bw%7D%20%7D)
V=![\frac{24.9}{1}](https://tex.z-dn.net/?f=%5Cfrac%7B24.9%7D%7B1%7D)
V=24.9 ![g/cm^{3}](https://tex.z-dn.net/?f=g%2Fcm%5E%7B3%7D)
Now bottle is partially filled with sand,and weight of bottle is (
)36.5gm
So,
Amount of sand added (
)=36.5-Weight of the bottle
=13g
After filling the bottle with water again,the weight of the bottle becomes (
=56.5g)
Therefore,
amount of water added to the bottle of sand in grams =
-36.5gm
amount of water added =56.5g-36.5g
amount of water added =20g
As the density of water = 1g/
Amount of water (in grams )=Volume of water occupied
20=volume of water added
Therfore volume of water added to the sand filled bottle(
)=20![cm^{3}](https://tex.z-dn.net/?f=cm%5E%7B3%7D)
As we know the total volume of the water bottle(V),
Volume of the sand occupied in the water bottle=V-![V_{w}](https://tex.z-dn.net/?f=V_%7Bw%7D)
=24.9g-20g
=4.9g
We know,
Density=Mass/Volume
Therefore,
density of sand = ![\frac{m_{s} }{V_{s} }](https://tex.z-dn.net/?f=%5Cfrac%7Bm_%7Bs%7D%20%7D%7BV_%7Bs%7D%20%7D)
density of sand =![\frac{13}{4.9}](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B4.9%7D)
density of sand = ![2.653g/cm^{3}](https://tex.z-dn.net/?f=2.653g%2Fcm%5E%7B3%7D)