Tag: properties of matter

Questions Related to properties of matter

A material capable of absorbing large amount of energy before fracture is known as 

elastic energy properties of material substances elasticity properties of matter physics

  1. Ductility

  2. Toughness

  3. Resilience

  4. Plasticity

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Correct Option: B
Explanation:

Toughness is the ability of a material to absorb energy and plastically deform without fracturing. 

It is defined as the amount of energy per unit volume that a material can absorb before rupturing.

The correct option is option(b)

A copper wire $1.0$ m and a steel wire of length $0.5$ m having equal cross-sectional areas are joining end to end. The composite wire is stretched by a certain load which stretches the copper wire by $1$ mm. If the Young's modulus  of copper steel are respectively $1.0\times 11^{11}Nm^{-1}$ and $ 2.0 \times 10^{11} Nm^{-2}$, the total extension of the composite wire is

elastic energy properties of material substances elasticity properties of matter physics

  1. $1.75mm$

  2. $2.0 mm$

  3. $1.50 mm$

  4. $1.25 mm$

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Correct Option: D

Give the MKS units for the following quantities.
Young's modulus.

elastic energy properties of material substances elasticity properties of matter physics

  1. $2N/m^2$.

  2. $3N/m^2$.

  3. $4N/m^2$.

  4. $N/m^2$.

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Correct Option: D

Two wires of different materials, each $2$m long and of diameter $2\,$mm, are joined in series to form a composite wire. What force will produce a total extension of $0.9$mm. $(Y _1=2\times 10^{11}\ Pa$ & $Y _2=6\times 10^{11}\ Pa)$.

elastic energy properties of material substances elasticity properties of matter physics

  1. $282.6$ N

  2. $212$ N

  3. $319.8$ N

  4. $382.6$ N

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Correct Option: B
Explanation:

Given.

Length of both wires, $L=2\,m$

Radius of both wires, $d=2mm=2\times {{10}^{-3}}m$

Total extension of joined wire, $\Delta {{L} _{net}}=0.9\,mm=9\times {{10}^{-4}}\,m$

Both wires join in series, so tension in both is equal

$T=\dfrac{{{Y} _{1}}A\Delta {{L} _{1}}}{L}=\dfrac{{{Y} _{2}}A\Delta {{L} _{2}}}{L}$  

Net extension in joined wire.

$\Rightarrow \Delta {{L} _{net}}=\Delta {{L} _{1}}+\Delta {{L} _{2}}=\dfrac{TL}{{{Y} _{1}}A}+\dfrac{TL}{{{Y} _{2}}A}=\dfrac{TL}{A}\left( \dfrac{1}{{{Y} _{1}}}+\dfrac{1}{{{Y} _{2}}} \right)$

$\Rightarrow \Delta {{L} _{net}}=\dfrac{TL}{A}\left( \dfrac{1}{{{Y} _{1}}}+\dfrac{1}{{{Y} _{2}}} \right)$

$\Rightarrow T=\dfrac{A\Delta {{L} _{net}}}{L\left( \dfrac{1}{{{Y} _{1}}}+\dfrac{1}{{{Y} _{2}}} \right)}=\dfrac{\dfrac{\pi }{4}{{\left( 2\times {{10}^{-3}} \right)}^{2}}\times 9\times {{10}^{-4}}}{2\left( \dfrac{1}{2\times {{10}^{11}}}+\dfrac{1}{6\times {{10}^{11}}} \right)}=212.05\ N$

Total force produced in joined wire is $212\ N$ 

Four identical hollow cylindrical columns of steel support a big structure of mass $50,000kg$. The inner and outer radii of each column are $30\ cm$ and $60\ cm$ respectively, Assuming the load distribution to be uniform. Calculate the compressional strain of each column,

elastic energy properties of material substances elasticity properties of matter physics

  1. $7.2\times 10^{-7}$

  2. $3.78\times 10^{-6}$

  3. $2.78\times 10^{-4}$

  4. $3.78\times 10^{-4}$

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Correct Option: A

To break a wire of 1 m length, minimum 40 kg weight is required. Then the wire of the same material of double radius and 6 m length will require breaking weight 

elastic energy properties of material substances elasticity properties of matter physics

  1. 80 kg weight

  2. 240 kg weight

  3. 200 kg weight

  4. 160 kg weight

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Correct Option: B

two wires of different material, each $2m$ long and of diameter $2mm$ are joined in series to form a composite wire.What force will produce a total extension of $0.9mm$ $\left( { Y } _{ 1 }=2\times { 10 }^{ 11 }N/{ m }^{ 2 },{ Y } _{ 2 }=7\times { 10 }^{ 11 }N/{ m }^{ 2 } \right) $

elastic energy properties of material substances elasticity properties of matter physics

  1. $22 N$

  2. $220 N$

  3. $120 N$

  4. 159 N$

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Correct Option: B

Which of the following shows greater increment in length when subjected to same load to wires made of same material:

elastic energy properties of material substances elasticity properties of matter physics

  1. $L = 1 m$ and $r = 1 mm$

  2. $L = 1 m$ and $r = 2 mm$

  3. $L = 2 m$ and $r = 1 mm$

  4. $L = 2 m$ and $r = 2 mm$

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Correct Option: A

A composite wire consists of a steel Wire of length 1 5 and a co uniform cross-sectional area of ${ 2.5\times  }10^{ -5 }{ m }^{ -5 }$.It is loaded with a mass of 200kg. Find the extension produced. Young's modulus of copper is ${ 2.5\times }10^{ 11 }{ Nm }^{ -2 }$ and that of steel ${ 2.0\times  }10^{ 11 }{ Nm }^{ -2 }$

elastic energy properties of material substances elasticity properties of matter physics

  1. 4.156 mm.

  2. 2.156 mm.

  3. 2.256 mm.

  4. 3.156 mm.

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Correct Option: B

A uniform rod of length L , area of cross-section A , mass m and Young 's modulus Y is pulled on  horizontal surface by a force f , such that the friction acting on it is F/2 . What if the elongation in the rod? 

elastic energy properties of material substances elasticity properties of matter physics

  1. $\frac { FL }{ 2AY } $

  2. $\frac { FL }{ AY }$

  3. $\frac { 3FL }{ 2AY }$

  4. $\frac { 3FL }{ 4AY }$

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Correct Option: A