Tag: forces and matter

Questions Related to forces and matter

A rubber cord 10 m is suspended vertically . How much does is stretch under its own weight (density of rubber is $1500kg{ m }^{ -3 },Y=5\times { 10 }^{ 8 }{ Nm }^{ -2 },g={ ms }^{ -2 }$)

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

  1. $15\times { 10 }^{ -4 }m\quad $

  2. $7.5\times { 10 }^{ -4 }m\quad $

  3. $12\times { 10 }^{ -4}m $

  4. $25\times { 10 }^{ -4 }m\quad $

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Correct Option: B

A copper wire of $1mm$ diameter is stretched by applying a force on $10N$. Find the stress in the wire.

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

  1. $1.273\times 10^7N/m^2$

  2. $1.373\times 10^7N/m^2$

  3. $1.473\times 10^7N/m^2$

  4. $1.573\times 10^7N/m^2$

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Correct Option: A

When the inter molecular distance increases due to tensile force, then 

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

  1. There is no force between the molecules

  2. There is a repulsive force between the molecules

  3. There is an attractive force between the molecules

  4. There is zero resultant force between the molecules

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Correct Option: C

A steel rod of length $5\ m$ is fixed rigidly between two supports, $\alpha$ of steel$=12\times 10^{-6}/^{o}\ C$, $Y=2\times10^{12}Nm^{-2}$. With the increase in its temperature by $40^{o}\ C$, the stress developed in the rod is

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

  1. $9.6\times10^{5}\ Nm^{-2}$

  2. $9.6\times10^{6}\ Nm^{-2}$

  3. $9.6\times10^{7}\ Nm^{-2}$

  4. $9.6\times10^{8}\ Nm^{-2}$

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Correct Option: C

A bar of cross-section A is subjected to equal and opposite tensile forces at its ends. Consider a plane section of the bar whose normal makes an angle $\theta$ with the axis of the bar.
For what value of $\theta$ is the tensile stress maximum?

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

  1. 0

  2. 1

  3. cant say

  4. 90

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Correct Option: A
Explanation:
Tensile stress$=\cfrac { force }{ area } =\cfrac { F\cos { \theta  }  }{ A\sec { \theta  }  } $
$=\cfrac { F }{ A } \cos ^{ 2 }{ \theta  } $
Tensile strength will be maximum when $\cos ^{ 2 }{ \theta  } $ is maximum i.e., $\cos { \theta  } =1$ or $\theta =0°$

A composite rod is 1000 mm long, its two ends are 40 $mm^2$ and 30 $mm^2$ in area and length are 300 mm and 200 mm respectively. The middle portion of the rod is 20 $mm^2$ in area and 500 mm long. If the rod is subjected to an axial tensile load of 1000 N, find its total elongation (in mm). (E = 200 GPa).

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

  1. 0.165

  2. 0.111

  3. 0.196

  4. none of the above

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Correct Option: C
Explanation:

$k=\dfrac{EA}{L}$

$k _1=\dfrac{EA _1}{L _1}$,$k _2=\dfrac{EA _2}{L _2}$,$k _3=\dfrac{EA _3}{L _3}$
$k _1=E\times \dfrac{40}{300} \times 10^{-3}$
$k _2=E\times \dfrac{30}{200} \times 10^{-3}$
$k _3=E\times \dfrac{20}{500} \times 10^{-3}$
$k _1=\dfrac{4E}{3} \times 10^{-4}$
$k _1=\dfrac{3E}{3} \times 10^{-4}$
$k _1=\dfrac{2E}{3} \times 10^{-4}$
$k _1,k _2,k _3$ are in series.
$\dfrac{1}{k _{eq}}=\dfrac{1}{k _1}+\dfrac{1}{k _2}+\dfrac{1}{k _3}$
$=\dfrac{3\times 10^4}{4E}$+$\dfrac{2\times 10^4}{3E}$+$\dfrac{5\times 10^4}{2E}$
$=\dfrac{10^4}{E}(\dfrac{3}{4}+\dfrac{2}{3}+\dfrac{5}{2})$
$=\dfrac{10^4}{E} \times \dfrac{47}{12}$
$k _{eq}=\dfrac{12E}{47} \times 10^{-4}$
$F=1000N$
$1000=\dfrac{12E}{47}\times 10^{-4} \Delta l$
$\Delta l=\dfrac{1000 \times 47}{12E}\times 10^4$
$\Delta l=\dfrac{1000\times 47 \times 10^4}{12\times 200 \times 10^9}$
$=19.6\times 10^{-5}$
$=0.196 mm$

A steel wire AB of length 100 cm is fixed rigidly at points A and B in an aluminium frame as shown in the figure If the temperature of the system increases through 100C, then the excess stress produced in the steel wire relative to the aluminium? ${ \alpha } _{ \mu }=22\times { 10 }^{ -6 }{ / }^{ 0 }Cand{ \alpha } _{ stret }=11\times { 10 }^{ -6 }{ / }^{ 0 }C$ young 's modulus of steel is $2\times { 10 }^{ 31 }{ Nm }^{ -2 }$

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

  1. $2.2\times { 10 }^{ 5 }$Pa

  2. $22\times { 10 }^{ 2 }$Pa

  3. $2.2\times { 10 }^{ 2 }$Pa

  4. $220\times { 10 }^{ 2 }$Pa

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Correct Option: C

A metal wire of length L, area of cross-section A and Young modulus Y behaves as a spring of spring constant

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

  1. $K= \frac{YA}{L}$

  2. $K= \frac{2YA}{L}$

  3. $K= \frac{YA}{2L}$

  4. $K= \frac{YL}{A}$

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Correct Option: A

A steel rod of length $1m$ and radius $10mm$ is stretched by a force $100kN$ along its length. The stress produced in the rod is then
 $\left( { Y } _{ steel }=2\times { 10 }^{ 11 }N\quad { m }^{ -2 } \right) $

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

  1. $3.18\times { 10 }^{ 6 }N\quad { m }^{ -2 }$

  2. $3.18\times { 10 }^{ 7 }N\quad { m }^{ -2 }\quad $

  3. $3.18\times { 10 }^{ 8 }N\quad { m }^{ -2 }$

  4. $3.18\times { 10 }^{ 9 }N\quad { m }^{ -2 }\quad $

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Correct Option: C
Explanation:

Here $r=10mm=10\times { 10 }^{ -3 }m={ 10 }^{ -2 }m$
$L=1m,F=100kN=100\times { 10 }^{ 3 }N={ 10 }^{ 5 }N$

Stress produced in the rod is:
$Stress=\cfrac { F }{ A } =\cfrac { F }{ \pi { r }^{ 2 } } =\cfrac { 100\times { 10 }^{ 3 }N }{ 3.14\times { \left( { 10 }^{ -2 }m \right)  }^{ 2 } } =3.18\times { 10 }^{ 8 }N\quad { m }^{ -2 }\quad $

One end of a uniform wire of length L and of weight W is attached rigidly to a point in the roof and
a weight $W _{1}$ is suspended from its lower end. If S is the are of cross-section of the wire, the stress in
the wire at a height (3 L /4) from its lower end is :

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

  1. $W _{1}/S$

  2. $[W _{1}+(W/4)]/S$

  3. $[W _{1}+(3W/4)]/S$

  4. $W _{1}+(W)/S$

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Correct Option: C