Tag: properties of substances

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Questions Related to properties of substances

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

A body of uniform cross-sectional area floats in a liquid of dentisty thrice its value. The portion of exposed height will be:

  1. 2/3

  2. 5/6

  3. 1/6

  4. 1/3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For floating body: weight = buoyant force. Ah₁ρ_body g = Ah₂ρ_liquid g, where h₁ is total height and h₂ is submerged height. Given ρ_liquid = 3ρ_body, we get h₁ = 3h₂. Exposed height = h₁ - h₂ = 2h₂ = 2/3 h₁. Option A is correct.

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

A cylindrical tree has a breaking stress of $10^6\ N/m^2$. The maximum possible height of the tree is $5\ m$. the density of material of the tree is (take $g = 10\ m/s^2$)

  1. $10^3\ kg/m^3$
  2. $10^4\ kg/m^3$
  3. $2 \times 10^4\ kg/m^3$
  4. $1\ kg/m^3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Breaking stress = Force / Area = (Mass * g) / Area = (Volume * density * g) / Area. Since Volume = Area * height, stress = density * g * height. Solving for density: 10^6 = density * 10 * 5, so density = 2 * 10^4 kg/m^3.

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

A block of ice floats on a liquid of density $1.2$ in a beaker then level of liquid when ice completely melt.

  1. Remains same

  2. Rises

  3. Lowers

  4. Either (b) or (c)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rises.

The level of the liquid in the beaker will rise. This is because the density of the water formed by the melting of ice is less than that of the density of liquid in the beaker 

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

An orifice of radius $r$ is present at the bottom of a container $r$. The maximum height to which the container can be filled with a liquid of density $\rho$ for which liquid will not come out of the orifice is?

  1. $\dfrac {T}{r\rho g}$
  2. $\dfrac {3T}{r\rho g}$
  3. $\dfrac {2T}{r\rho g}$
  4. $\dfrac {4T}{r\rho g}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For liquid not to overflow or leak out through an orifice due to surface tension, the upward force created by surface tension must balance the downward hydrostatic pressure force. The pressure at depth h is rho*g*h, and the force due to surface tension along the perimeter of radius r is 2*pi*r*T. Equating the upward force (2*pi*r*T) to the downward force (rho*g*h * pi*r^2) yields the maximum height h = 2T/(r*rho*g).

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

A rectangular block 5m x 4m x 2m lies on a table with its largest surface in contact with the table. The work done to keep it so that the block rests on the smallest surface is, if its density is 600 k $m ^ { - 3 }$

  1. $352800 \mathrm { J }$

  2. zero
  3. $376000 \mathrm { J }$
  4. $24,0000 \mathrm { J }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of Rectangular block $ = 5m \times 4m \times 2m$

$ = 40\,\,{m^3}$
Mass = Volume $ \times$ Density
$\begin{array}{l} =40\, \, { m^{ 3 } }\times 600\, \, k{ m^{ -3 } } \ =24,000=2.4\times { 10^{ 4 } }\, \, hg \end{array}$
Potential energy of block when it is lying on its largest surface $= mgh$
$ = 2.4 \times {10^4} \times 9.8 \times 1\,\,joule$
Potential energy of the block when it is lying on 
$ = mgh = 2.4 \times {10^4} \times 9.8 \times 2.5$
Work done = difference in potential energy
$\begin{array}{l} =\left( { 2.4\times { { 10 }^{ 4 } }\times 9.8\times 2.5-2.4\times { { 10 }^{ 4 } }\times 9.8\times 1 } \right) joule \ =2.4\times { 10^{ 4 } }\times 9.8\times 1.5\, \, joule \ =352800\, \, joule \end{array}$
Option A

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

When two liquid of same volume but different densities $\rho _{1}$ and $\rho _{2}$ are mixed together, then the density of the mixture is

  1. $\dfrac {p _{1}+p _{2}}{2}$
  2. $p _{1}+p _{2}$
  3. $\dfrac {2p _{1}p _{2}}{p _{1}+p _{2}}$
  4. $2p _{1}+2p _{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$Density \,\,of \,\,mixture = \dfrac{Total\,\, mass }{ Total \,\,volume}$

Let $1^{st}$ liquid have mass $M _1$, density $p _1$ and Volume $V$

and
$2^{st}$ liquid have mass $M _2$, density $p _2$ and Volume $V$
So,Density of mixture  $= \dfrac{M _1 +M _2}{2V}$$=$$\dfrac {p _1V+p _2V}{2V}$

                                 $\rho _m=\dfrac{p _1+p _2}{2}$

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

If the length of the cylinder is measured as 25 mm, the diameter is 3.09cm and mass of the cylinder is measured as 50.0 gm find the density of the cylinder in proper significant figures.(in $gm/cm^3$)

  1. 2.700 $gm/cm^3$
  2. 2.7 $gm/cm^3$
  3. 0.27 $gm/cm^3$
  4. 2.70$gm/cm^3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$p\, =\, \displaystyle \frac{m}{\pi (d^2\, /\, 4)h}$
$p\, =\, \displaystyle \frac{(50.0) gm}{3.14\, \times\, (3.09/2)^2\, \times\, (25\, \times\, 10^{-1}) cm^3}\, =\, 2.7\, gm/cm^3$
(in two S.F.)

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

The greatest length of the wire made of material of breaking stress $ 8 \times 10^8 N/m^2 $ and density $ 8 \times 10^3kg m^3 $ that can be suspended from a rigid support without breaking is $ ( g= 10m/s^2) $ 

  1. $1 km$
  2. $0.1 km$
  3. $10 km$
  4. $20$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$ stress= length \times desity \times g $
$ length = \dfrac {stress}{g \times density} $
$= \dfrac { 8 \times 10^8}{10 \times 8 \times 10^3 } $


$=10km$

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

A tank  $5 { m }$  high is half filled with water and then is filled to the top with oil of density  $0.85 g / c m ^ { 3 } .$  The pressure at the bottom of the tank, due to these liquids is

  1. $1.85{ g }/{ cm }^{ { 2 } }$
  2. $89.25{ g }/{ cm }^{ { 2 } }$
  3. $462.5{ g }/{ cm }^{ { 2 } }$
  4. $500{ g }/{ cm }^{ { 2 } }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given,

Total height of tank $=5\,m$

Density of water, $\rho _1=1\,g/cm^3$

Density of oil, $\rho _2=0.85\,g/cm^3$

We know that,

Half tank is filled with water and half tank is filled with oil.

So,  $h _1=h _2=\dfrac 52=2.5\,m=250\,cm$

Pressure at the bottom of the tank is

$P=h _1\rho _1g+h _2\rho _2g$

$P=g(250\times 1+250\times 0.85)$

$P=462.5\,g/cm^2$