Grade 11 : Physics - Solids (Set 2)

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Grade 11 : Physics - Solids (Set 2)— Questions & Detailed Solutions

A steel cable in an elevator system carries a total load of 500 N. The cross-sectional area of the cable is $2.5 \times 10^{-4}m^2$.
Calculate the tensile stress developed inside the cable.

(A)

$2.0 \times 10^6\text{ N/m}^2$

(B)

$1.25 \times 10^5\text{ N/m}^2$

(C)

$5.0 \times 10^6\text{ N/m}^2$

(D)

$4.0 \times 10^5\text{ N/m}^2$

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✓ Correct Option: (A)

Explanation: Tensile stress is defined as force per unit cross-sectional area: $\text{Stress} = \frac{F}{A} = \frac{500\text{ N}}{2.5 \times 10^{-4}m^2} = 2.0 \times 10^6\text{ N/m}^2$.

A metal rod of original length 4 m is pulled in a testing lab, resulting in an elongation of 2 mm.
What is the longitudinal strain experienced by the rod?

(A)

$5.0 \times 10^{-3}$

(B)

$5.0 \times 10^{-4}$

(C)

$2.0 \times 10^{-3}$

(D)

$8.0 \times 10^{-4}$

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✓ Correct Option: (B)

Explanation: Longitudinal strain is given by the change in length divided by initial length: $\text{Strain} = \frac{\Delta L}{L} = \frac{2 \times 10^{-3}m}{4m} = 5.0 \times 10^{-4}$.

A suspension bridge wire experiences a tensile stress of $4.0 \times 10^8\text{ N/m}^2$, resulting in a strain of $2.0 \times 10^{-3}$.
Determine the Young's Modulus of the material of the wire.

(A)

$8.0 \times 10^{11}\text{ N/m}^2$

(B)

$1.0 \times 10^{11}\text{ N/m}^2$

(C)

$2.0 \times 10^{11}\text{ N/m}^2$

(D)

$5.0 \times 10^{10}\text{ N/m}^2$

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: Young's Modulus $Y$ is stress divided by strain: $Y = \frac{\text{Stress}}{\text{Strain}} = \frac{4.0 \times 10^8}{2.0 \times 10^{-3}} = 2.0 \times 10^{11}\text{ N/m}^2$.

During a laboratory demonstration, students measure the deformation of various structural components.
Which of the following is the SI unit of longitudinal strain?

(A)

$\text{N/m}^2$

(B)

$\text{Pascal (Pa)}$

(C)

$\text{Meter (m)}$

(D)

Dimensionless (No units)

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✓ Correct Option: (D)

Explanation: Strain is the ratio of change in length to initial length ($\Delta L / L$). Being a ratio of two identical quantities, strain is dimensionless and unitless.

Hooke's Law governs small deformations of elastic materials.
According to Hooke's Law, within the elastic limit, stress is:

(A)

Directly proportional to strain

(B)

Inversely proportional to strain

(C)

Proportional to the square of strain

(D)

Independent of strain

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✓ Correct Option: (A)

Explanation: Hooke's Law states that for small deformations within the elastic limit, stress is directly proportional to strain ($\text{Stress} \propto \text{Strain}$).

A solid metal sphere submerged in a deep oceanic trench experiences a uniform hydraulic pressure increase of $2.0 \times 10^6\text{ Pa}$, causing a fractional change in volume $\frac{\Delta V}{V} = 1.0 \times 10^{-4}$.
What is the Bulk Modulus of the metal sphere?

(A)

$2.0 \times 10^2\text{ Pa}$

(B)

$2.0 \times 10^{10}\text{ Pa}$

(C)

$5.0 \times 10^{-11}\text{ Pa}$

(D)

$1.0 \times 10^8\text{ Pa}$

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Bulk Modulus $B = \frac{\Delta P}{\Delta V / V} = \frac{2.0 \times 10^6\text{ Pa}}{1.0 \times 10^{-4}} = 2.0 \times 10^{10}\text{ Pa}$.

Engineers compare fluid and solid responses under compression.
How is the compressibility of a material defined?

(A)

Direct product of Young's modulus and strain

(B)

Equal to the Shear modulus

(C)

Reciprocal of Bulk modulus

(D)

Ratio of shear stress to volumetric strain

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✓ Correct Option: (C)

Explanation: Compressibility $k$ is defined mathematically as the reciprocal of the Bulk Modulus ($k = \frac{1}{B}$).

A metal block of height 0.1 m has its bottom surface fixed while a shearing force is applied parallel to the top surface, displacing it horizontally by 0.02 mm.
Calculate the shear strain experienced by the block.

(A)

$2.0 \times 10^{-4}\text{ rad}$

(B)

$5.0 \times 10^{-3}\text{ rad}$

(C)

$2.0 \times 10^{-2}\text{ rad}$

(D)

$1.0 \times 10^{-5}\text{ rad}$

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✓ Correct Option: (A)

Explanation: Shear strain $\theta = \frac{\Delta x}{h} = \frac{0.02 \times 10^{-3}m}{0.1m} = 2.0 \times 10^{-4}\text{ rad}$.

A high-strength steel rod is subjected to a uniform tensile stress of $1.0 \times 10^8\text{ N/m}^2$, producing a strain of $5.0 \times 10^{-4}$.
Calculate the elastic strain energy stored per unit volume of the rod.

(A)

$5.0 \times 10^4\text{ J/m}^3$

(B)

$1.0 \times 10^5\text{ J/m}^3$

(C)

$5.0 \times 10^3\text{ J/m}^3$

(D)

$2.5 \times 10^4\text{ J/m}^3$

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✓ Correct Option: (D)

Explanation: Elastic energy density $u = \frac{1}{2} \times \text{Stress} \times \text{Strain} = \frac{1}{2} \times (1.0 \times 10^8) \times (5.0 \times 10^{-4}) = 2.5 \times 10^4\text{ J/m}^3$.

Q10

A technician pulls a spring-steel wire with a constant tension force of 200 N, stretching it by 3 mm.
What is the total work done in stretching the wire?

(A)

0.6 J

(B)

0.3 J

(C)

1.2 J

(D)

0.15 J

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✓ Correct Option: (B)

Explanation: Work done in stretching a wire is $W = \frac{1}{2} F \Delta L = \frac{1}{2} \times 200\text{ N} \times (3 \times 10^{-3}m) = 0.3\text{ J}$.

Q11

When a cylinder is stretched along its axis, its cross-sectional radius decreases slightly.
Poisson's ratio is defined as the ratio of:

(A)

Lateral strain to longitudinal strain

(B)

Longitudinal strain to lateral strain

(C)

Shear stress to shear strain

(D)

Volumetric strain to longitudinal strain

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✓ Correct Option: (A)

Explanation: Poisson's ratio $\sigma$ is defined as the ratio of lateral strain (transverse contraction) to longitudinal strain (axial elongation).

Q12

Consider theoretical considerations for homogeneous isotropic elastic materials.
What is the theoretical range of Poisson's ratio ($\sigma$)?

(A)

$0\text{ to } 1$

(B)

$-0.5\text{ to } 1$

(C)

$-1\text{ to } 0.5$

(D)

$0\text{ to } 0.5$

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✓ Correct Option: (C)

Explanation: The theoretical limits of Poisson's ratio for an isotropic elastic solid lie strictly between -1 and 0.5.

Q13

A student compares a steel wire and a rubber band of identical dimensions under equal stretching forces.
Why is steel considered more elastic than rubber in physics?

(A)

Steel requires a much larger force for the same strain, giving it a higher Young's modulus

(B)

Rubber can stretch much further before breaking

(C)

Steel breaks easily under tension

(D)

Rubber returns faster to original shape than steel

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✓ Correct Option: (A)

Explanation: Elasticity is measured by the magnitude of Young's Modulus ($Y = \text{Stress}/\text{Strain}$). Steel offers greater restoring stress per unit strain than rubber, so steel is more elastic.

Q14

A material undergoes mechanical stress testing until failure.
A material that breaks or fractures almost immediately after passing its elastic limit is called:

(A)

Ductile

(B)

Brittle

(C)

Elastomer

(D)

Malleable

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✓ Correct Option: (B)

Explanation: Brittle materials exhibit very little to no plastic deformation past the elastic limit and fracture suddenly.

Q15

A steel rod of length 1.5 m, cross-sectional area $1.0 \times 10^{-4}m^2$, and Young's modulus $Y = 2.0 \times 10^{11}\text{ N/m}^2$ acts as a structural spring.
What is the effective force constant ($k$) of this rod?

(A)

$3.0 \times 10^7\text{ N/m}$

(B)

$2.0 \times 10^7\text{ N/m}$

(C)

$1.33 \times 10^7\text{ N/m}$

(D)

$7.5 \times 10^6\text{ N/m}$

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: From Hooke's Law, $F = \left(\frac{YA}{L}\right) \Delta L$, so force constant $k = \frac{YA}{L} = \frac{(2.0 \times 10^{11})(1.0 \times 10^{-4})}{1.5} = 1.33 \times 10^7\text{ N/m}$.

Q16

An engineering standard specifies breaking stress for structural wires.
The breaking stress (tensile strength) of a wire of given material depends primarily on:

(A)

Length of the wire

(B)

Radius of cross-section

(C)

Shape of cross-section

(D)

Material property of the wire

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✓ Correct Option: (D)

Explanation: Breaking stress is an intrinsic characteristic property of the material, independent of geometric dimensions like length or radius.

Q17

A rigid structural steel beam fixed firmly between two unyielding concrete supports is cooled or heated. The linear thermal expansion coefficient $\alpha = 1.2 \times 10^{-5}\text{ K}^{-1}$, Young's modulus $Y = 2.0 \times 10^{11}\text{ N/m}^2$, and temperature change $\Delta T = 50^\circ\text{C}$.
Calculate the thermal stress developed in the beam.

(A)

$2.4 \times 10^7\text{ N/m}^2$

(B)

$1.2 \times 10^8\text{ N/m}^2$

(C)

$6.0 \times 10^8\text{ N/m}^2$

(D)

$1.2 \times 10^6\text{ N/m}^2$

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Thermal stress is given by $\text{Stress} = Y \alpha \Delta T = (2.0 \times 10^{11}) \times (1.2 \times 10^{-5}) \times 50 = 1.2 \times 10^8\text{ N/m}^2$.

Q18

A rubber strip is repeatedly loaded and unloaded, producing a stress-strain hysteresis loop.
What physical quantity is represented by the area enclosed within the elastic hysteresis loop?

(A)

Thermal energy dissipated per unit volume per cycle

(B)

Total elastic potential energy permanently stored

(C)

Breaking stress of the rubber strip

(D)

Young's modulus of the rubber

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✓ Correct Option: (A)

Explanation: The area inside an elastic hysteresis loop measures the mechanical energy converted to heat (dissipated) per unit volume during a full cycle of loading and unloading.

Q19

A long heavy uniform wire of length $L$, density $\rho$, and Young's modulus $Y$ hangs vertically from a high ceiling under gravity $g$.
What is the total elongation produced in the wire due to its own weight?

(A)

$\frac{\rho g L^2}{Y}$

(B)

$\frac{2 \rho g L^2}{Y}$

(C)

$\frac{\rho g L^2}{2 Y}$

(D)

$\frac{\rho g L}{2 Y}$

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✓ Correct Option: (C)

Explanation: Effective weight acts at the center of gravity ($L/2$). Integrating tension along the length gives total elongation $\Delta L = \frac{\rho g L^2}{2Y}$.

Q20

Consider the elastic deformation of a cylinder subjected to tangential surface forces.
The Modulus of Rigidity (Shear Modulus $\eta$) is defined as the ratio of:

(A)

Tensile stress to longitudinal strain

(B)

Hydraulic pressure to volume strain

(C)

Tensile stress to shear strain

(D)

Shearing stress to shearing strain

View Correct Answer & Detailed Solution

✓ Correct Option: (D)

Explanation: Modulus of Rigidity (or Shear Modulus $\eta$) is defined as the ratio of shearing stress to shearing strain.

Grade 11 : Physics - Solids (Set 2)

Grade 11 : Physics - Solids (Set 2)— Questions & Detailed Solutions

A steel cable in an elevator system carries a total load of 500 N. The cross-sectional area of the cable is $2.5 \times 10^{-4}m^2$.
Calculate the tensile stress developed inside the cable.

A metal rod of original length 4 m is pulled in a testing lab, resulting in an elongation of 2 mm.
What is the longitudinal strain experienced by the rod?

A suspension bridge wire experiences a tensile stress of $4.0 \times 10^8\text{ N/m}^2$, resulting in a strain of $2.0 \times 10^{-3}$.
Determine the Young's Modulus of the material of the wire.

During a laboratory demonstration, students measure the deformation of various structural components.
Which of the following is the SI unit of longitudinal strain?

Hooke's Law governs small deformations of elastic materials.
According to Hooke's Law, within the elastic limit, stress is:

A solid metal sphere submerged in a deep oceanic trench experiences a uniform hydraulic pressure increase of $2.0 \times 10^6\text{ Pa}$, causing a fractional change in volume $\frac{\Delta V}{V} = 1.0 \times 10^{-4}$.
What is the Bulk Modulus of the metal sphere?

Engineers compare fluid and solid responses under compression.
How is the compressibility of a material defined?

A metal block of height 0.1 m has its bottom surface fixed while a shearing force is applied parallel to the top surface, displacing it horizontally by 0.02 mm.
Calculate the shear strain experienced by the block.

A high-strength steel rod is subjected to a uniform tensile stress of $1.0 \times 10^8\text{ N/m}^2$, producing a strain of $5.0 \times 10^{-4}$.
Calculate the elastic strain energy stored per unit volume of the rod.

A technician pulls a spring-steel wire with a constant tension force of 200 N, stretching it by 3 mm.
What is the total work done in stretching the wire?

When a cylinder is stretched along its axis, its cross-sectional radius decreases slightly.
Poisson's ratio is defined as the ratio of:

Consider theoretical considerations for homogeneous isotropic elastic materials.
What is the theoretical range of Poisson's ratio ($\sigma$)?

A student compares a steel wire and a rubber band of identical dimensions under equal stretching forces.
Why is steel considered more elastic than rubber in physics?

A material undergoes mechanical stress testing until failure.
A material that breaks or fractures almost immediately after passing its elastic limit is called:

A steel rod of length 1.5 m, cross-sectional area $1.0 \times 10^{-4}m^2$, and Young's modulus $Y = 2.0 \times 10^{11}\text{ N/m}^2$ acts as a structural spring.
What is the effective force constant ($k$) of this rod?

An engineering standard specifies breaking stress for structural wires.
The breaking stress (tensile strength) of a wire of given material depends primarily on:

A rubber strip is repeatedly loaded and unloaded, producing a stress-strain hysteresis loop.
What physical quantity is represented by the area enclosed within the elastic hysteresis loop?

A long heavy uniform wire of length $L$, density $\rho$, and Young's modulus $Y$ hangs vertically from a high ceiling under gravity $g$.
What is the total elongation produced in the wire due to its own weight?

Consider the elastic deformation of a cylinder subjected to tangential surface forces.
The Modulus of Rigidity (Shear Modulus $\eta$) is defined as the ratio of:

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Grade 11 : Physics - Solids (Set 2)

Grade 11 : Physics - Solids (Set 2)— Questions & Detailed Solutions

A steel cable in an elevator system carries a total load of 500 N. The cross-sectional area of the cable is $2.5 \times 10^{-4}m^2$.Calculate the tensile stress developed inside the cable.

A metal rod of original length 4 m is pulled in a testing lab, resulting in an elongation of 2 mm.What is the longitudinal strain experienced by the rod?

A suspension bridge wire experiences a tensile stress of $4.0 \times 10^8\text{ N/m}^2$, resulting in a strain of $2.0 \times 10^{-3}$.Determine the Young's Modulus of the material of the wire.

During a laboratory demonstration, students measure the deformation of various structural components.Which of the following is the SI unit of longitudinal strain?

Hooke's Law governs small deformations of elastic materials.According to Hooke's Law, within the elastic limit, stress is:

A solid metal sphere submerged in a deep oceanic trench experiences a uniform hydraulic pressure increase of $2.0 \times 10^6\text{ Pa}$, causing a fractional change in volume $\frac{\Delta V}{V} = 1.0 \times 10^{-4}$.What is the Bulk Modulus of the metal sphere?

Engineers compare fluid and solid responses under compression.How is the compressibility of a material defined?

A metal block of height 0.1 m has its bottom surface fixed while a shearing force is applied parallel to the top surface, displacing it horizontally by 0.02 mm.Calculate the shear strain experienced by the block.

A high-strength steel rod is subjected to a uniform tensile stress of $1.0 \times 10^8\text{ N/m}^2$, producing a strain of $5.0 \times 10^{-4}$.Calculate the elastic strain energy stored per unit volume of the rod.

A technician pulls a spring-steel wire with a constant tension force of 200 N, stretching it by 3 mm.What is the total work done in stretching the wire?

When a cylinder is stretched along its axis, its cross-sectional radius decreases slightly.Poisson's ratio is defined as the ratio of:

Consider theoretical considerations for homogeneous isotropic elastic materials.What is the theoretical range of Poisson's ratio ($\sigma$)?

A student compares a steel wire and a rubber band of identical dimensions under equal stretching forces.Why is steel considered more elastic than rubber in physics?

A material undergoes mechanical stress testing until failure.A material that breaks or fractures almost immediately after passing its elastic limit is called:

A steel rod of length 1.5 m, cross-sectional area $1.0 \times 10^{-4}m^2$, and Young's modulus $Y = 2.0 \times 10^{11}\text{ N/m}^2$ acts as a structural spring.What is the effective force constant ($k$) of this rod?

An engineering standard specifies breaking stress for structural wires.The breaking stress (tensile strength) of a wire of given material depends primarily on:

A rubber strip is repeatedly loaded and unloaded, producing a stress-strain hysteresis loop.What physical quantity is represented by the area enclosed within the elastic hysteresis loop?

A long heavy uniform wire of length $L$, density $\rho$, and Young's modulus $Y$ hangs vertically from a high ceiling under gravity $g$.What is the total elongation produced in the wire due to its own weight?

Consider the elastic deformation of a cylinder subjected to tangential surface forces.The Modulus of Rigidity (Shear Modulus $\eta$) is defined as the ratio of:

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A steel cable in an elevator system carries a total load of 500 N. The cross-sectional area of the cable is $2.5 \times 10^{-4}m^2$.
Calculate the tensile stress developed inside the cable.

A metal rod of original length 4 m is pulled in a testing lab, resulting in an elongation of 2 mm.
What is the longitudinal strain experienced by the rod?

A suspension bridge wire experiences a tensile stress of $4.0 \times 10^8\text{ N/m}^2$, resulting in a strain of $2.0 \times 10^{-3}$.
Determine the Young's Modulus of the material of the wire.

During a laboratory demonstration, students measure the deformation of various structural components.
Which of the following is the SI unit of longitudinal strain?

Hooke's Law governs small deformations of elastic materials.
According to Hooke's Law, within the elastic limit, stress is:

A solid metal sphere submerged in a deep oceanic trench experiences a uniform hydraulic pressure increase of $2.0 \times 10^6\text{ Pa}$, causing a fractional change in volume $\frac{\Delta V}{V} = 1.0 \times 10^{-4}$.
What is the Bulk Modulus of the metal sphere?

Engineers compare fluid and solid responses under compression.
How is the compressibility of a material defined?

A metal block of height 0.1 m has its bottom surface fixed while a shearing force is applied parallel to the top surface, displacing it horizontally by 0.02 mm.
Calculate the shear strain experienced by the block.

A high-strength steel rod is subjected to a uniform tensile stress of $1.0 \times 10^8\text{ N/m}^2$, producing a strain of $5.0 \times 10^{-4}$.
Calculate the elastic strain energy stored per unit volume of the rod.

A technician pulls a spring-steel wire with a constant tension force of 200 N, stretching it by 3 mm.
What is the total work done in stretching the wire?

When a cylinder is stretched along its axis, its cross-sectional radius decreases slightly.
Poisson's ratio is defined as the ratio of:

Consider theoretical considerations for homogeneous isotropic elastic materials.
What is the theoretical range of Poisson's ratio ($\sigma$)?

A student compares a steel wire and a rubber band of identical dimensions under equal stretching forces.
Why is steel considered more elastic than rubber in physics?

A material undergoes mechanical stress testing until failure.
A material that breaks or fractures almost immediately after passing its elastic limit is called:

A steel rod of length 1.5 m, cross-sectional area $1.0 \times 10^{-4}m^2$, and Young's modulus $Y = 2.0 \times 10^{11}\text{ N/m}^2$ acts as a structural spring.
What is the effective force constant ($k$) of this rod?

An engineering standard specifies breaking stress for structural wires.
The breaking stress (tensile strength) of a wire of given material depends primarily on:

A rubber strip is repeatedly loaded and unloaded, producing a stress-strain hysteresis loop.
What physical quantity is represented by the area enclosed within the elastic hysteresis loop?

A long heavy uniform wire of length $L$, density $\rho$, and Young's modulus $Y$ hangs vertically from a high ceiling under gravity $g$.
What is the total elongation produced in the wire due to its own weight?

Consider the elastic deformation of a cylinder subjected to tangential surface forces.
The Modulus of Rigidity (Shear Modulus $\eta$) is defined as the ratio of: