Selina solutions

Selina solutions

Grade 8

Physical Quantities and Measurement | Numericals

Question 9

Q9) The mass of an empty density bottle is 21.8 g, when filled completely with water is 41.8 g and when filled completely with liquid is 40.6 g. Find:

(a) The volume of density bottle

(b) the relative density of liquid

  • Solution

  • Transcript

Solution:

Density of water = 1 g cm³

(a) Volume of density bottle

Mass of empty density bottle = M1 = 21.8g

Mass of bottle + water = M2 = 41.8g

So, mass of water completely filling the density bottle = M2-M1

= 41.8 - 21.8 = 20g

1g of water has volume =cc

So, Volume of bottle = volume of water = 20cc = 20ml

(b) The relative density of liquid

Mass of 20 cc of liquid

= (mass of density bottle + mass of 20cc of liquid) - mass of density bottle

= 40.6 - 21.8

= 18.8 g

Mass of 20 cc of water = 20g

Relative density of liquid

R.D = \frac{Mass\ of\ 20\ cc\ of\ liquid}{Mass\ of\ 20\ cc\ of\ water}=\frac{18.8}{20}=0.94\

hello students welcome to Lido learning's question and answer videos let's have a look at this question the question says the mass of an empty density bottle is 21.8 grams when filled completely with water then the mass is 41.8 grams and when completely filled with a liquid the mass is 40.6 grams to make this question more clearer i have a picture of a density bottle here so we should first know what do we mean by a density bottle right before proceeding to the question so a density bottle looks like this it has a stopper and a hole so what is the purpose of this hole so when we fill this bottle with liquid whenever there is any liquid which is extra it just comes out from this particular hole as you can see the extra liquid comes out from this therefore the volume of the liquid is the same every time it is filled so it will always have the volume will be constant or the same whatever liquid you fill in this bottle the volume will be same so now we have to calculate how much volume is it for this particular density bottle and also the relative density of liquid so before that there are three cases given here right which is the mass of an empty density bottle so let's keep the density bottle on a to weigh the mass and we have it is 21.8 grams so we know mars is given as 21.8 grams okay next is the density bottle is filled with water so let's say it has been filled with water so the mass now is 41.8 grams as you can see here in the picture so the mass is 41.8 grams so now what will be the mass of the water which is completely filling the density bottle so to find out that so the empty density the bottle is 21.8 grams and so let me just write that down so empty density bottle let's say it's m1 the mass is 21.8 grams then we have filled the density bottle filled with water right so when it is filled with water the mass are 41.8 grams so the mass of water straight away we can find out is 41.8 minus 21.8 that is the empty density right and empty density bottles mass so we could get this as 20 grams okay now we have got the mass of water in this, we have to find the volume right as according to question number a or part a we have to find a volume so we all know that density of water is how much incidence yes it is one gram per centimeter cube so if it is 20 grams then it will be the volume occupied by that bottle will be 20-centimeter cube we know density how do we get that we know that density is equal to mass upon volume so here the density of water is one gram per centimeter cube you put in place of density you put one is equal to we know the mass is 20 and we don't know the volume of water so let's keep it as the liquid which is 18.8 grams upon the mass of the same volume of water so the mass of the water was 20 grams right so let's just write that down as 20 below and we get the answer as to how much do we get zero-point when we calculate we get 0.94 now what do we place or what units will the relative density be so we see here that there are no units for relative density, it's a ratio since it's a ratio the above is the mass which is in grams below also we have a mass which is in grams so they just cancel out and what do we get here 0.94 as the answer so the relative density of the liquid that is part b of the question is equal to 0.94 and part a that is the volume of the density bottle is a 20-centimeter cube everywhere so i hope this question was clear the understanding of the concept was clear if you have any further doubts, please post your comments below thank you

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Question 9

Q9) The mass of an empty density bottle is 21.8 g, when filled completely with water is 41.8 g and when filled completely with liquid is 40.6 g. Find:

(a) The volume of density bottle

(b) the relative density of liquid

  • Solution

  • Transcript

Solution:

Density of water = 1 g cm³

(a) Volume of density bottle

Mass of empty density bottle = M1 = 21.8g

Mass of bottle + water = M2 = 41.8g

So, mass of water completely filling the density bottle = M2-M1

= 41.8 - 21.8 = 20g

1g of water has volume =cc

So, Volume of bottle = volume of water = 20cc = 20ml

(b) The relative density of liquid

Mass of 20 cc of liquid

= (mass of density bottle + mass of 20cc of liquid) - mass of density bottle

= 40.6 - 21.8

= 18.8 g

Mass of 20 cc of water = 20g

Relative density of liquid

R.D = \frac{Mass\ of\ 20\ cc\ of\ liquid}{Mass\ of\ 20\ cc\ of\ water}=\frac{18.8}{20}=0.94\

hello students welcome to Lido learning's question and answer videos let's have a look at this question the question says the mass of an empty density bottle is 21.8 grams when filled completely with water then the mass is 41.8 grams and when completely filled with a liquid the mass is 40.6 grams to make this question more clearer i have a picture of a density bottle here so we should first know what do we mean by a density bottle right before proceeding to the question so a density bottle looks like this it has a stopper and a hole so what is the purpose of this hole so when we fill this bottle with liquid whenever there is any liquid which is extra it just comes out from this particular hole as you can see the extra liquid comes out from this therefore the volume of the liquid is the same every time it is filled so it will always have the volume will be constant or the same whatever liquid you fill in this bottle the volume will be same so now we have to calculate how much volume is it for this particular density bottle and also the relative density of liquid so before that there are three cases given here right which is the mass of an empty density bottle so let's keep the density bottle on a to weigh the mass and we have it is 21.8 grams so we know mars is given as 21.8 grams okay next is the density bottle is filled with water so let's say it has been filled with water so the mass now is 41.8 grams as you can see here in the picture so the mass is 41.8 grams so now what will be the mass of the water which is completely filling the density bottle so to find out that so the empty density the bottle is 21.8 grams and so let me just write that down so empty density bottle let's say it's m1 the mass is 21.8 grams then we have filled the density bottle filled with water right so when it is filled with water the mass are 41.8 grams so the mass of water straight away we can find out is 41.8 minus 21.8 that is the empty density right and empty density bottles mass so we could get this as 20 grams okay now we have got the mass of water in this, we have to find the volume right as according to question number a or part a we have to find a volume so we all know that density of water is how much incidence yes it is one gram per centimeter cube so if it is 20 grams then it will be the volume occupied by that bottle will be 20-centimeter cube we know density how do we get that we know that density is equal to mass upon volume so here the density of water is one gram per centimeter cube you put in place of density you put one is equal to we know the mass is 20 and we don't know the volume of water so let's keep it as the liquid which is 18.8 grams upon the mass of the same volume of water so the mass of the water was 20 grams right so let's just write that down as 20 below and we get the answer as to how much do we get zero-point when we calculate we get 0.94 now what do we place or what units will the relative density be so we see here that there are no units for relative density, it's a ratio since it's a ratio the above is the mass which is in grams below also we have a mass which is in grams so they just cancel out and what do we get here 0.94 as the answer so the relative density of the liquid that is part b of the question is equal to 0.94 and part a that is the volume of the density bottle is a 20-centimeter cube everywhere so i hope this question was clear the understanding of the concept was clear if you have any further doubts, please post your comments below thank you

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