Tag: properties of matter

Questions Related to properties of matter

A liquid is contained in a vessel. The liquid-solid adhesive force is very as compared to the liquid. The shape of the liquid surface will be

intermolecular forces: cohesive and adhesive forces surface tension properties of matter physics

  1. Horizontal

  2. Vertical

  3. Concave

  4. Convex

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Correct Option: A
Explanation:

If the liquid solid adhesive force is same as that of liquid then the surface will be horizontal at zero angle of contact.

On a clean glass plate a drop of water spreads to form a thin layer whereas a drop of mercury remains almost spherical because

intermolecular forces: cohesive and adhesive forces surface tension properties of matter physics

  1. mercury is a metal

  2. density of mercury is greater than that of water

  3. cohesion of mercury is greater than its adhesion with glass

  4. cohesion of water is greater than its adhesion with glass

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Correct Option: C
Explanation:

Mercury remains spherical on a glass plate due to greater cohesive force between mercury molecules than adhesive force between mercury and glass plate.

A capillary tube of radius $0.25\ mm$ is submerged vertically in water so that $25\ mm$ of its length outside water. The radius of curvature of the meniscus will be $(T = 7.5\times 10^{-3} N/m)$.

intermolecular forces: cohesive and adhesive forces surface tension properties of matter physics

  1. $0.2\ mm$

  2. $0.4\ mm$

  3. $0.6\ mm$

  4. $0.8\ mm$

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Correct Option: C
Explanation:

$h= \dfrac{2T}{dgx}$

$h= \dfrac{2\times 7.5 \times {10}^-3} {1000 \times 10 \times d}$
$h=25mm$
$d= 0.6 mm$

A cable that can support a load of 800 N is cut into two equal parts. The maximum load that can be supported by either part is 

forces on solids elastic and plastic substances forces and matter properties of matter physics

  1. 100 N

  2. 400 N

  3. 800 N

  4. 1600 N

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Correct Option: C
Explanation:

Breaking stress $= \dfrac{800 N}{A} \Rightarrow BA$

  $F = 800 N$
Breaking stress doesn't depend upon the length of the cable.

A uniform steel bar of cross-sectional area A and length L. is suspended so that it hangs vertically. The stress at the middle point of the bar is ( $\rho $ is the density of steel)

forces on solids elastic and plastic substances forces and matter properties of matter physics

  1. $\frac{L}{2A} \rho g$

  2. $\frac{L\rho g}{2} $

  3. $\frac{LA}{\rho g}$

  4. $L\rho g$

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Correct Option: C

On suspending a weight $Mg$ the length $l$ of elastic wire and area of cross section $A$ its length becomes double the initial length. The instantaneous stress action on the wire is:

forces on solids elastic and plastic substances forces and matter properties of matter physics

  1. $\dfrac{Mg}{A}$

  2. $\dfrac{Mg}{2A}$

  3. $\dfrac{2Mg}{A}$

  4. $\dfrac{4Mg}{A}$

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Correct Option: C

The velocity of the transverse waves in a wire of density $8000kg/m^3$ is $300 m/s$. The tensile stress in the wire is then

forces on solids elastic and plastic substances forces and matter properties of matter physics

  1. $7.2\times10^8 N/m^2$

  2. $6.8\times10^8 N/m^2$

  3. $5.2\times10^8 N/m^2$

  4. $8.4\times10^8 N/m^2$

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Correct Option: A
Explanation:

Given density = 8000 $kg/{ m }^{ 3 }$ and velocity =300 m/s

Also we know velocity of transverse wave  $\text{V}=\sqrt { \dfrac { T }{ \mu  }  } \text{where T= tension and}\quad \mu =\text{mass per unit lenght}\quad =\dfrac { m }{ L } \quad $
also $\text{Density}\quad \rho =\dfrac { mass }{ Area\times Lenght } \ \rho \times A=\dfrac { m }{ L } $
$\text{Tension T}=\rho A{ V }^{ 2 }$
We know stress $\sigma =\dfrac { Force }{ Area } =\dfrac { Tension }{ Area } =\dfrac { { V }^{ 2 }\rho A }{ A } ={ V }^{ 2 }\rho $
${ 300 }^{ 2 }\times 8000=7.2\times { 10 }^{ 8 }\dfrac { N }{ { m }^{ 2 } } $ 

An external force of $10\ N$ acts normally on a square area of each side $50\ cm$. The stress produced in equilibrium state is

forces on solids elastic and plastic substances forces and matter properties of matter physics

  1. $10\ N/m^{2}$

  2. $20\ N/m^{2}$

  3. $40\ N/m^{2}$

  4. $50\ N/m^{2}$

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Correct Option: C

The length of wire is increased by $0.06\%$ by a load of $40N$ whose tensile modulus is $20\times10^{10}N/M^2$.The subjected stress is 

forces on solids elastic and plastic substances forces and matter properties of matter physics

  1. $12\times10^{10}N/m^2$

  2. $1.2\times10^{8}N/m^2$

  3. $120N/m^2$

  4. $1.25\times10^6N/m^2$

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Correct Option: B
Explanation:

$\cfrac{\triangle l}{l}\times 100=0.06$

$\implies \cfrac{\triangle l}{l}=\cfrac{0.06}{100}$
Now stress $=\cfrac{20\times 10^{10}\times 0.06}{1000}\=1.2\times 10^8\ N /m^2$

According to $C.E$ van der Waal, the interatomic potential varies with the average interatomic distance $(R)$ as 

forces on solids elastic and plastic substances forces and matter properties of matter physics

  1. $R^{-1}$

  2. $R^{-2}$

  3. $R^{-4}$

  4. $R^{-6}$

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Correct Option: D
Explanation:

According to the relation

$ V(r)=\dfrac{-3}{4}\dfrac{{{\alpha }^{2}} _{0}l}{{{(4\pi {{\varepsilon } _{0}})}^{2}}{{R}^{6}}} $

$ V(r)\propto \dfrac{1}{{{R}^{6}}} $

$ V(r)\propto {{R}^{-6}} $