Tag: properties of substances

Questions Related to properties of substances

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

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

  1. 2/3

  2. 5/6

  3. 1/6

  4. 1/3

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Correct Option: A

The surface density of charge on a large flat metal plate is $2.25 x { 10 }^{ 9 } coul/{m}^{2}$. The intensity of electric field at a point at a distance $20 cm$ from the plate is

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

  1. $90\pi N/C$

  2. $180\pi N/C$

  3. $45\pi N/C$

  4. $81\pi N/C$

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Correct Option: A

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 $g = 10\ m/s^2$)

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

  1. $10^3\ kg/m^3$

  2. $10^4\ kg/m^3$

  3. $2 \times 10^4\ kg/m^3$

  4. $1\ kg/m^3$

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Correct Option: C

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

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

  1. Remains same

  2. Rises

  3. Lowers

  4. Either (b) or (c)

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Correct Option: B
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 

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?

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

  1. $\dfrac {T}{r\rho g}$

  2. $\dfrac {3T}{r\rho g}$

  3. $\dfrac {2T}{r\rho g}$

  4. $\dfrac {4T}{r\rho g}$

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Correct Option: A

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 $m ^ { - 3 }$

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

  1. $352800 \mathrm { J }$

  2. zero

  3. $376000 \mathrm { J }$

  4. $24,0000 \mathrm { J }$

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Correct Option: A
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

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

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

  1. $\dfrac {p _{1}+p _{2}}{2}$

  2. $p _{1}+p _{2}$

  3. $\dfrac {2p _{1}p _{2}}{p _{1}+p _{2}}$

  4. $2p _{1}+2p _{2}$

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Correct Option: A
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}$

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

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 $gm/cm^3$)

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

  1. 2.700 $gm/cm^3$

  2. 2.7 $gm/cm^3$

  3. 0.27 $gm/cm^3$

  4. 2.70$gm/cm^3$

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Correct Option: B
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.)

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) $ 

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

  1. $1 km$

  2. $0.1 km$

  3. $10 km$

  4. $20$

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Correct Option: C
Explanation:

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


$=10km$

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

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

  1. $1.85{ g }/{ cm }^{ { 2 } }$

  2. $89.25{ g }/{ cm }^{ { 2 } }$

  3. $462.5{ g }/{ cm }^{ { 2 } }$

  4. $500{ g }/{ cm }^{ { 2 } }$

Show answer
Correct Option: C
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

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

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

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