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Compressive and tensile forces - class-XII

Description: compressive and tensile forces
Number of Questions: 16
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Tags: properties of matter mechanical properties of solids physics forces and matter properties of bulk matter matter and materials
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Assertion (A): Steel is more elastic than rubber.
Reason (R) : Under a given deforming force, steel is deformed less than rubber.


A) Both Assertion and Reason are true and the reason is correct explanation of the assertion
B)Both Assertion and Reason are true, but reason is not correct explanation of the assertion
C) Assertion is true, but the reason is false
D) Assertion is false, but the reason is true

physics hooke's law

  1. A

  2. B

  3. C

  4. D

Show answer
Correct Option: A
Explanation:

More elastic the material, higher the Young's Modulus.
Young's Modulus of Steel = 200 GPa
Young's Modulus of Rubber = 0.01-0.1 GPa
Young's Modulus of Steel is much higher than Rubber, So steel is more elastic than rubber.

Y = FL/Al
Y - Young's Modulus
L - Actual Length
A - Cross Section Area
l - Elongation

l = FL/AY
keeping F,L,A constant 
l is inversely proportional to Y
Hence, Higher the Young's Modulus lesser the deformation (for Different Materials)

Change in the shape of a body caused by the application of a force (stress) is called as :

physics hooke's law

  1. ductility

  2. deformation

  3. hardness

  4. rigidity

Show answer
Correct Option: B
Explanation:

If a force on a body changes the normal positions of the molecules of a body, resulting in a change in the configuration of the body, then the force applied is called deforming force and change in shape of the body is called deformation. 

Change in shape of a body caused by the application of stress is called:

physics hooke's law

  1. rigidity

  2. elasticity

  3. sheer

  4. deformation

Show answer
Correct Option: D
Explanation:

Deformation of a body is the change in shape of a body caused by the application of stress. According to the Hooke's law, the deformation caused in an elastic material is directly proportional to the stress applied to it.

State whether true or false :
While loading the crane with heavy bodies, it is given rest from time to time.

physics hooke's law

  1. True

  2. False

Show answer
Correct Option: A

State whether true or false :
The property of an elastic body by virtue of which its behaviour becomes less elastic under the action of repeated alternating deforming force is called elastic fatigue

physics hooke's law

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Elastic fatigue is defined as the temporary loss of elastic properties of a material by applying repeated force on the material. If there is no sufficient time between repeated force application, then a permanent deformation remain there in each time of applying force.

If stress-strain relation for volumetric change is in the form $\cfrac { \Delta V }{ { V } _{ 0 } } =KP$ where $P$ is applied uniform pressure, then $K$ stands for

physics hooke's law

  1. shear modulus

  2. compressibility

  3. Young's modulus

  4. bulk modulus

Show answer
Correct Option: B
Explanation:

Bulk modulus $=\cfrac { P }{ \Delta V/V } $
Compressibility$=\cfrac { 1 }{ Bulk\quad modulus } =\cfrac { \Delta V/V }{ P } =K\quad \quad $(Compressibility)

 Time dependent permanent deformation is called

physics hooke's law

  1. Plastic deformation

  2. Elastic deformation

  3. Creep

  4. Anelastic deformation

Show answer
Correct Option: C
Explanation:

Creep is a situation in which a component experiences deformation with time as it is put into use. Best example to illustrate this is that electrical cables are taught(tight) when they are installed but after some time they experience sagging due to self weight.

The correct option is option (c)

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 W1 is suspended from its lower end. of S is true area of cross section of the wire, the stress in the wire at a height (3L/4) from its lower end is:

physics hooke's law

  1. [W1 + (W/4)]/S

  2. W1/S

  3. [W1 + (3W/4)]/S

  4. (W1 + W)/S

Show answer
Correct Option: C

When a steel rod of length 2m is compressed its length decreases by 0.1m. Find the work done against the compressive stress.$\left( { Y } _{ steel }=2.0\times { 10 }^{ 11 }{ Nm }^{ -2 } \right) $

physics hooke's law

  1. $2.5\times { 10 }^{ 11 } J $

  2. $1.25\times { 10 }^{ 11 } J $

  3. $5.0\times { 10 }^{ 11 } J $

  4. $7.5\times { 10 }^{ 4 } J $

Show answer
Correct Option: A

Four wires of the same material are stretched by the same load. The dimension are given below.Which of them will elongate the most?

physics hooke's law

  1. ${\text{Length}}\;100{\text{cm}},{\text{diameter}}\;1{\text{mm}}$

  2. ${\text{Length}}\;200{\text{cm}},{\text{diameter}}\;2{\text{mm}}$

  3. ${\text{Length}}\;300{\text{cm}},{\text{diameter}}\;3{\text{mm}}$

  4. ${\text{Length}}\;400{\text{cm}},{\text{diameter}}\;0.5{\text{mm}}$

Show answer
Correct Option: C

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

Show answer
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

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

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

Show answer
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

Show answer
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

Show answer
Correct Option: E
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