Tag: forces and matter

Questions Related to forces and matter

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}} $


Overall changes in volume and radii of a uniform cylindrical steel wire are $0.2\% $ and $0.002\%$ respectively when subjected to some suitable force. Longitudinal tensile stress acting on the wire is $\left( {Y = 2.0 \times {{10}^{11}}N{m^{ - 2}}} \right)$

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

  1. $3.2 \times {10^9}N{m^{ - 2}}$

  2. $3.2 \times {10^7}N{m^{ - 2}}$

  3. $3.6 \times {10^9}N{m^{ - 2}}$

  4. $3.6 \times {10^7}N{m^{ - 2}}$

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Correct Option: C

A steel wire has an ultimate strength of above $2.0 \times 10 ^ { 7 } \mathrm { kg } - \mathrm { w } \mathrm { J } / \mathrm { m } ^ { 2 }$ . How large a load can a
0.7$\mathrm { cm }$ in diameter steel wire hold before breaking?

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

  1. $700 \mathrm { kg } - \mathrm { wt }$

  2. $770 \mathrm { kg } - \mathrm { wt }$

  3. $300 \mathrm { kg } - \mathrm { wt }$

  4. None

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Correct Option: A

If equal and opposite forces applied to a body tend to elongate it, the stress so produced is called

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

  1. Tensile stress

  2. Compressive stress

  3. Tangential stress

  4. Working stress

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Correct Option: A