Tag: fundamental and derived units

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Questions Related to fundamental and derived units

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

Which of the following is true about the density of a substance?

  1. It is a derived quantity.
  2. The unit of density in SI system is kilogram per metre$^3$.

  3. The density of a substance can be measured if the mass of the substance for a certain volume is known.

  4. Density is a vector quantity.
Reveal answer Fill a bubble to check yourself
A,B,C Correct answer
Explanation

The density of a substance is defined as the mass of the substance per unit volume of the substance.
$\rho=\dfrac mV$

Its unit is $kg/m^3$

It is a derived quantity as it uses the unit of mass and the unit of length.
The unit of density in the SI system is kilogram per meter $^3$.
The density of a substance can be measured if the mass of the substance for a certain volume is known.

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

A vessel contains oil (density $= 0.8\ gm/cm^{3})$ over mercury (density $= 13.6\ gm/ cm^{3})$. A uniform sphere floats with half its volume immersed in mercury and the other half in oil. The density of the material of sphere in $gm/ cm^{3}$ is

  1. $3.3$
  2. $6.4$
  3. $7.2$
  4. $12.8$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A vessel contains oil density $=0.8gm/cm^3$

Mercury density $=13.6gm/cm^3$
Total weight is balanced by the displaced volumes of the two different fluids. Let it $s$ and volume id $v$ and te density is $n$.
Then the equilibrium condition should be
$v _{mg}=v/2(0.8)g+\cfrac{v}{2\times136g}\n=0.4+6.8=7.2gm/cm^3$

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

The heart of man pumps 5 litre of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury. If the density of mercury be $13.6 \times 10^3 \ kg/m^3$ and g = 10 m/$s^2$ then the power of heart in watt is: 

  1. $2.35$
  2. $3.0$
  3. $1.50$
  4. $1.70$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Power = Pressure × (Volume/Time). Pressure = ρgh = (13.6×10³ kg/m³)(10 m/s²)(0.150 m) = 20,400 Pa. Flow rate = 5 L/min = 5×10⁻³ m³/60 s = 8.33×10⁻⁵ m³/s. Power = (20,400)(8.33×10⁻⁵) = 1.70 W. Option D is correct.

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

A boat floating in a tank is carrying passenger. If the passangers drink water, how will its affect the water level of the tank?

  1. It will go down

  2. It will rise

  3. It will remain unchanged

  4. It will depend on atmospheric pressure
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If passenger drinks water then the weight of boat get increase and the boat will displace the same amount of water in the tank resulting no net change in the water level.

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

Density of water is ___________?

  1. $1000kg/m^3$
  2. $1kg/m^3$
  3. $1000g/cm^2$
  4. $100kg/m^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Density of water is $1000kg/m^3$.

ρ (rho) = density, m = mass, V = volume. The SI unit of density is kg/m3. Water of 4 °C is the reference ρ = 1000 kg/m3 = 1 kg/dm3 = 1 kg/l or 1 g/cm3 = 1 g/ml.

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

A tank $2\ m$ high is half filled with water and then filled to the top with oil of density $0.80\ g/cc$. What is the pressure at the bottom of the tank due to these liquids (Take $g=10\ ms^{-2}$) is

  1. $1.80\times 10^{3}\ Nm^{-2}$
  2. $0.9\times 10^{3}\ Nm^{-2}$
  3. $1.8\times 10^{4}\ Nm^{-2}$
  4. $0.9\times 10^{4}\ Nm^{-2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Density of oil=0.80 g/cc=800 kg/m$^{3}$

Density of water=1 g/cc=1000 kg/m$^{3}$
Pressure of water=Height will be 1 m half filled
$\Longrightarrow hdg=1 m \times 1000 kg/m^{3} \times 10m/s^{2}=10000 Pa$
Pressure by oil$=hdg$
Total pressure$=(1 \times 8000 \times 10)=8000 Pa+10000 Pa = 18000 Pa=1.8 \times 10^{4} N/m^{2}$

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

Density of ice is $\sigma$ and that of water is $\rho$. What will be the decrease in volume when a mass $M$ of ice melts 

  1. $\dfrac {M}{\sigma - \rho}$
  2. $\dfrac {\sigma - \rho}{M}$
  3. $M\left [\dfrac {1}{\sigma} - \dfrac {1}{\rho}\right ]$
  4. $M\left [\dfrac {1}{\rho} - \dfrac {1}{\sigma}\right ]$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of ice= Mass/Density= $M/P$

Volume of water= Mass/Density= $M/\sigma$
Decrease in volume= $V _i-V _w$
$=\cfrac {M}{P}-\cfrac {M}{\sigma}= M\left[\cfrac {1}{P}-\cfrac {1}{\sigma}\right]$

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

By sucking through a straw, a boy can reduce the pressure in his lungs to $750\ mm$ of $Hg$ (density$ = 13.6\,\,g/c{m^3}$). Using a straw, he can drink water from a maximum depth of

  1. $13.6\ cm$
  2. $1.36\ cm$
  3. $0.136\ cm$
  4. $10\ cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given Pressure in lungs${P} _{lungs}=750$ mm of Hg

and atmospheric pressure${P} _{atm}=760$ mm of Hg
Now pressure difference $\Delta{P}=760-750=10$ mm of Hg=1 cm of Hg
Now
1 cm of Hg$={\rho} _{water}gh$
$1{\rho} _{Hg}g={\rho} _{water}gh$
$13.6g=gh$
$h=13.6 cm$