Tag: hooke's law

Questions Related to hooke's law

Four identical hollow cylindrical columns of steel support a big structure of mass $50,000$ kg. The inner and outer radii of each column are $30$cm and $40$cm respectively.Assuming the load distribution to be uniform. Calculate the compressional strains of each column, the young's modulus of steel is $2 \times {10^{11}}Pa$

physics hooke's law

  1. $2.78 \times {10^{ - 6}}$

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

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

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

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Correct Option: C

An elastic metal rod will change its length when it

physics hooke's law

  1. falls vertically under its weight

  2. is pulled along its length by a force acting at one end

  3. rotates about an axis at one end

  4. slides on a rough surface

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Correct Option: B,C
Explanation:

An elastic metal rod will change its length when it is pulled along its length by a force acting at one end or rotates about an axis at one end. Since, deforming force exceeds the elastic limit.

Length of a wire is increased by 1 mm on the application of a given load. If same load is applied to another wire of same material but of length and radius twice that of the first then increase in its length will be 

physics hooke's law

  1. $2 mm$

  2. $\dfrac{1}{2} mm$

  3. $4 mm$

  4. $\dfrac{1}{4} mm$

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Correct Option: B
Explanation:

$\dfrac{{stress}}{{strain}} = y$

$strain = \dfrac{{stress}}{y}$
$\dfrac{{\Delta l}}{l} = \dfrac{f}{{\Delta y}}$
$\Delta l = \dfrac{f}{y} \cdot \dfrac{l}{A}$
$\Delta l' = \dfrac{f}{y} \cdot \dfrac{{2l}}{{\pi \left( {2{r^2}} \right)}}$
$\Delta l' = \dfrac{f}{y} \cdot \dfrac{{2l}}{{4A}}$
$\Delta l' = \dfrac{{\Delta l}}{2} = \dfrac{1}{2}mm$
Hence,
option $(B)$ is correct answer.

The maximum stress developed in the rod is equal to $(N/m^{2})$.

physics hooke's law

  1. $5\times 10^{7}$

  2. $5\times 10^{8}$

  3. $4\times 10^{7}$

  4. $4\times 10^{8}$

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Correct Option: C

Which of the following is/are true about deformation of a material?

physics hooke's law

  1. Deformation capacity of the plastic hinge and resilience of the connections are essential for good plastic behavior

  2. Deformation capacity equations considering yield stress and gradient of moment

  3. Different materials have different deformation capacity

  4. All of the above

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Correct Option: D
Explanation:

In well-designed steel frame structures, inelastic deformation under severe seismic loading is confirmed in beam plastic hinges located near the beam-to-column connections. Thus, deformation capacity of the plastic hinge and resilience of the connections are essential for good plastic behavior and expected energy dissipation in steel frame structures. This essential plastic behaviour at the hinge is strongly influenced by the difference of material properties. Generally, the material properties are specified in terms of yield stress and/or ultimate strength. However, the characteristics of the materials are not defined by only these properties. Thus, the characteristics of various materials aren’t reflected in present building codes, particularly on deformation capacity classification.

The sides at 960 mm of 4 g. By what distance (in cm) will be the column be displaced is the tube is held verticle

physics hooke's law

  1. 4 cm

  2. 6 cm

  3. 9 cm

  4. 3 cm

  5. None of these

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Correct Option: E