Tag: fundamental and derived units

Questions Related to fundamental and derived units

Brine has a density of 1.2 g/cc. 40 cc of it is mixed with 30 cc of water. The density of the resulting solution will be

chemistry substances in the surroundings - their states and properties measurement of density properties of substances fundamental and derived units

  1. $2.11$ g/cc

  2. $1.11$ g/cc

  3. $12.2$ g/cc

  4. $20.4$ g/cc

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Correct Option: B
Explanation:

Density of Brine$=\rho _{b}=1.2g/cc$

Volume of Brine$=v _{b}=40cc$
Mass of Brine$=m _{b}=\rho _{b}\times v _{b}=1.2\times 40=48g$
Density of Water$=\rho _{w}=1g/cc$
Volume of Water$=v _{w}=30cc$

Mass of Water$=m _{w}=\rho _{w}\times v _{w}=1\times 30=30g$
Density of mixture$=\dfrac{\text{Mass of mixture}}{\text{ Volume of mixture}}=\dfrac{m _{b}+m _{w}}{v _{b}+v _{w}}=\dfrac{48+30}{40+30}=\dfrac{78}{70}=1.11g/cc$

Calculate the mass of air enclosed in a room of length, breadth and height equal to $5\ m, 3 \ m$ and $4 \ m$ respectively. Density of air is $1.3 \ kg/m^3$.

chemistry substances in the surroundings - their states and properties measurement of density properties of substances fundamental and derived units

  1. $78 \ kg$

  2. $38 \ kg$

  3. $42 \  kg$

  4. $87 \ kg$

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Correct Option: A
Explanation:

The Volume of the room is given as $V = L\times B\times H= 5\times 3\times 4 = 60  { m }^{ 3 }.$
We know, Mass $=$ Density$\times$Volume.
Given that the density $=1.3  kg/m^3$.
So, Mass of the air $=1.3\times60  Kg$.
Hence, mass of the air enclosed in the room is 78 kg.

If the mass of a body is 12.1 g and the density is 2.2g/cc, its volume is :

chemistry substances in the surroundings - their states and properties measurement of density properties of substances fundamental and derived units

  1. $\displaystyle 5.5{ cm }^{ 3 }$

  2. $8 cc$

  3. $11 cc$

  4. $55 cc$

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Correct Option: A
Explanation:
density $\rho=\dfrac{mass}{ volume}$

$2.2=\dfrac{12.1}{volume}$

volume $=5.5{cm}^3$

The SI unit of density is $\displaystyle kg\ { m }^{ -3 }$. State whether true or false.

chemistry substances in the surroundings - their states and properties measurement of density properties of substances fundamental and derived units

  1. True

  2. False

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Correct Option: A
Explanation:
S.I unit of density is kg/${m}^3$
since, density=mass/volume

If two masses A and B have their masses in the ratio 1 : 4 and their volumes are equal, then their densities have the ratio

chemistry substances in the surroundings - their states and properties measurement of density properties of substances fundamental and derived units

  1. 1:4

  2. 8:1

  3. 2: 4

  4. 3:1

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Correct Option: A
Explanation:

Let mass of $A$ be $m$

Mass of $B$ be $4m$
Let density of $A$ be $d _a$
Density of $B$ be $d _b$
And Volume of A$=$Volume of B$=V$
As Density$=\dfrac{\text {Mass}}{\text {Volume}}$

Therefore $d _a=\dfrac{m}{V}$
$d _b=\dfrac{4m}{V}$

$\dfrac{d _a}{d _b}=\dfrac{\dfrac{m}{V}}{\dfrac{4m}{V}}$
$\dfrac{d _a}{d _b}=\dfrac{m}{4m}=\dfrac{1}{4}$
Hence the correct answer is option (A).

What is the density of an iron block which has a volume of ${12 cm^3}$ and a mass of 96g?

chemistry substances in the surroundings - their states and properties measurement of density properties of substances fundamental and derived units

  1. ${ 8 kg/m ^3}$

  2. ${80 kg /m ^3}$

  3. ${8000 kg /m ^3}$

  4. ${800 kg/ m ^3}$

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Correct Option: A
Explanation:

Answer is A.

As we know, Density $d = \dfrac{Mass, M}{ Volume, V}$


In this case, an iron block which has a volume of ${12 cm^3}$ = ${0.12 m^3}$ and a mass of $96 g = 0.096 kg$.

Therefore, Density $d =\dfrac{ 0.096}{0.12} = 8 kg/m^{ 3 }$.

Hence, the density of the iron block is 8 $kg/m^{ 3 }$.

The ratio of the values in SI units to values in CGS units of density is

chemistry substances in the surroundings - their states and properties measurement of density properties of substances fundamental and derived units

  1. $10^3:1$

  2. $10^2:1$

  3. $10^{-2}:1$

  4. $10^{-3}:1$

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Correct Option: A
Explanation:

the density of water in S.I. unit $\rho=1000 kg/{m}^3$

the density of water in CGS unit $\rho'=1 gm/cc$

the ratio of the densities of water in the different system 
$\dfrac{\rho}{\rho'}=\dfrac{{10}^3}{1}$

The density of water is $\displaystyle { 10 }^{ 3 }kg\ { m }^{ -3 }$. State whether true or false.

chemistry substances in the surroundings - their states and properties measurement of density properties of substances fundamental and derived units

  1. True

  2. False

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Correct Option: A
Explanation:

It is a fact that the density of water is 1000 kg / ${m}^3$

When air is cooled, its density increases. State whether true or false.

chemistry substances in the surroundings - their states and properties measurement of density properties of substances fundamental and derived units

  1. True

  2. False

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Correct Option: A
Explanation:

 As on cooling volume of air decreases and its mass remains constant so its density increases as  Density = $\dfrac{mass}{volume}$

hence given statement is correct so option (A) is correct

The hot air balloon rises because it is

chemistry substances in the surroundings - their states and properties measurement of density properties of substances fundamental and derived units

  1. denser

  2. less dense

  3. equally dense

  4. the given statement is wrong

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Correct Option: B
Explanation:

The hot air balloon has the hot air filled in it and the density of air is more than the hot air. So, the normal air or atmospheric air has the tendency to remain below than the hot air as the objects having the more density remains below than the objects having less density.