Students can refer to the following **MCQ on Mechanical Properties of Solids class 11 PDF** with Answers provided below based on the latest curriculum and examination pattern issued by CBSE and NCERT. Our teachers have provided here a collection of multiple-choice questions for Chapter 9 Mechanical Properties of Solids Class 11 Physics covering all topics in your textbook so that students can assess themselves on all important topics and thoroughly prepare for their exams

## MCQ on Mechanical Properties of Solids class 11 PDF with Answers

We have provided below MCQ on Mechanical Properties of Solids class 11 PDF with answers which will help the students to go through the entire syllabus and practice multiple choice questions provided here with solutions. As MCQ Questions for Class 11 Physics pdf download can be really scoring for students, you should go through all problems provided below so that you are able to get more marks in your exams.

**Question. The bulk modulus of a spherical object is ‘B’. If it is subjected to uniform pressure ‘p’, the fractional decrease in radius is **

(a) B/3p

(b) 3p/B

(c) p/3B

(d) p/B

**Answer**

C

**Question. The Young’s modulus of steel is twice that of brass.****Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of**

(a) 4 : 1

(b) 1 : 1

(c) 1 : 2

(d) 2 : 1

**Answer**

D

**Question. The approximate depth of an ocean is 2700 m. ****The compressibility of water is 45.4 × 10 ^{–11} Pa^{–1} and density of water is 10^{3} kg/m3. What fractional compression of water will be obtained at the bottom of the ocean?**

(a) 1.2 × 10

^{–2}

(b) 1.4 × 10

^{–2}

(c) 0.8 × 10

^{–2}

(d) 1.0 × 10

^{–2}

**Answer**

A

**Question. Copper of fixed volume V is drawn into wire of length l. When this wire is subjected to a constant force F, the extension produced in the wire is Dl. Which of the following graphs is a straight line?**

(a) Dl versus 1/l

(b) Dl versus l 2

(c) Dl versus 1/l 2

(d) Dl versus l

**Answer**

B

**Question. The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied? **

(a) length = 200 cm, diameter = 2 mm

(b) length = 300 cm, diameter = 3 mm

(c) length = 50 cm, diameter = 0.5 mm

(d) length = 100 cm, diameter = 1 mm

**Answer**

C

**Question. Elastomers are the materials which **

(a) are not elastic at all

(b) have very small elastic range

(c) do not obey Hooke’s law

(d) None of these

**Answer**

C

**Question. Which of the following affects the elasticity of a substance? **

(a) hammering and annealing

(b) change in temperature

(c) impurity in substance

(d) All of these

**Answer**

D

**Question. Which of the following has no dimensions ? **

(a) strain

(b) angular velocity

(c) momentum

(d) angular momentum

**Answer**

A

**Question. Minimum and maximum values of Possion’s ratio for a metal lies between **

(a) – ∞ to + ∞

(b) 0 to 1

(c) – ∞ to 1

(d) 0 to 0.5

**Answer**

D

**Question. In solids interatomic forces are **

(a) totally repulsive

(b) totally attractive

(c) both (a) and (b)

(d) None of these

**Answer**

C

**Question. When a pressure of 100 atmosphere is applied on a spherical ball, then its volume reduces to 0.01%. The bulk modulus of the material of the rubber in dyne/cm ^{2} is **

(a) 10 × 10

^{12}

(b) 100 × 10

^{12}

(c) 1 × 10

^{12}

(d) 10 × 10

^{12}

**Answer**

C

**Question. What per cent of length of wire increases by applying a stress of 1 kg weight/mm ^{2} on it? **

**(Y = 1 × 10**

^{11}N/m^{2}and 1 kg weight = 9.8 newton)(a) 0.0067%

(b) 0.0098%

(c) 0.0088%

(d) 0.0078%

**Answer**

B

**Question. K is the force constant of a spring. The work done in increasing its extension from l_{1} to l_{2} will be **

(a) K(

*l*

_{2}–

*l*

_{1})

(b) K/2(

*l*

_{2}+

*l*

_{1})

(c) K(

*l*

_{2}

^{2}–

*l*

_{1}

^{2})

(d) K/2(

*l*

_{2}

^{2}+

*l*

_{1}

^{2})

**Answer**

D

**Question. Two wires of same material and length but cross-sections in the ratio 1 : 2 are used to suspend the same loads. The extensions in them will be in the ratio **

(a) 1 : 2

(b) 2 : 1

(c) 4 : 1

(d) 1 : 4

**Answer**

B

**Question. A body of mass 10 kg is attached to a wire of radius 3 cm. It’s breaking stress is 4.8 × 10 ^{7} Nm^{–2}, the area of cross-section of the wire is 10^{–6} m^{2}. What is the maximum angular velocity with which it can be rotated in the horizontal circle ? **

(a) 1 rad sec

^{–1}

(b) 2 rad sec

^{–1}

(c) 4 rad sec

^{–1}

(d) 8 rad sec

^{–1}

**Answer**

C

**Question. The Young’s modulus of brass and steel are respectively 10 ^{10} N/m^{2}. and 2 × 10^{10} N/m^{2}. A brass wire and a steel wire of the same length are extended by 1 mm under the same force, the radii of brass and steel wires are RB and RS respectively. Then**

(a) R

_{S}= √2 R

_{B}

(b) R

_{S}= R

_{B}/√2

(c) R

_{S}= 4R

_{B}

(d) R

_{S}= R

_{B}/ 4

**Answer**

B

**Question. A polyster fibre rope of diameter 3 cm has a breaking strength of 150 kN. If it is required to have 600 kN breaking strength. What should be the diameter of similar rope?**

(a) 12 cm

(b) 6 cm

(c) 3 cm

(d) 1.5 cm

## Answer

B

**Question. One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is**

(a) 0.25

(b) 0.50

(c) 2.00

(d) 4.00

## Answer

C

**Question. The following four wires of length L and radius r are made of the same material. Which of these will have the largest extension, when the same tension is applied?**

(a) L = 100 cm, r = 0.2 mm

(b) L = 200 cm, r = 0.4 mm

(c) L = 300 cm, r = 0.6 mm

(d) L = 400 cm, r = 0.8 mm

## Answer

A

**Question. A mild steel wire of length 2L and crosssectional area A is stretched, well within elastic limit, horizontally between two pillars as shown in the figure. A mass m is suspended from the mid‑point of the wire. Strain in the wire is**

(a) x^{2}/2L^{2}

(b) x/L

(c) x^{2}/L

(d) x^{2}/2L

## Answer

A

**Question. Two blocks of masses 1 kg and 2 kg are connected by a metal wire going over a smooth pulley as shown in figure. The breaking stress of the metal is (40/3π) × 10 ^{6} N/m^{2}. If g = 10 m s^{–2}, then the minimum radius of the wire used if it is not to break is**

(a) 0.5 mm

(b) 1 mm

(c) 1.5 mm

(d) 2 mm

## Answer

B

**Question. Assuming that shear stress at the base of a mountain is equal to the force per unit area due to its weight. Calculate the maximum possible height of a mountain on the earth if breaking stress of a typical rock is 3 × 10 ^{8} N m^{–2} and its density is 3 × 103 kg m^{–3}.**

(Take g = 10 m s

^{–2})

(a) 4 km

(b) 8 km

(c) 10 km

(d) 16 km

## Answer

C

**Question. A solid sphere of radius R, made of a material of bulk modulus K, is surrounded by a liquid in a cylindrical container. A massless piston of area A floats on the surface of the liquid. When a mass M is placed on the piston to compress the liquid the fractional change in the radius of the sphere dR/R, is**

(a) Mg/2AK

(b) Mg/3AK

(c) Mg/AK

(d) 2Mg/3AK

## Answer

B

**Question. Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area A and wire 2 has crosssectional area 3A. If length of wire l is increased by Δx on applying force F, how much force is needed to stretch wire 2 by the same amount?**

(a) 4F

(b) 6F

(c) 9F

(d) F

## Answer

C

**Question. If Y and B represent Young’s modulus and bulk modulus for a material, then in practice**

(a) Y < 3B

(b) Y = 3B

(c) Y > 3B

(d) B = 3Y

## Answer

A

**Question. The Young’s modulus of brass and steel are respectively 1.0 × 10 ^{11} N m^{–2} and 2.0 × 10^{11} N m^{–2}. A brass wire and a steel wire of the same length are extended by 1 mm each under the same force. If radii of brass and steel wires are R_{B} and R_{S} respectively, then**

(a) R

_{S}= √2R

_{B}

(b) R

_{S}= R

_{B}/√2

(c) R

_{S}= 4R

_{B}

(d) R

_{S}= R

_{B}/2

## Answer

B

**Question. Two wires A and B of the same material have their lengths in the ratio of 1 : 2 and their diameters in the ratio of 2 : 1. If they are stretched with the same force, the ratio of the increase in the length of A to that of B will be**

(a) 1 : 2

(b) 4 : 1

(c) 1 : 8

(d) 1 : 4

## Answer

C

**Question. Two wires A and B have the same length and area of cross-section. But Young’s modulus of A is two times the Young’s modulus of B. Then the ratio of force constant of A to that of B is**

(a) 1

(b) 2

(c) 1/2

(d) √2

## Answer

B

**Question. A steel bar ABCD 40 cm long is made up of three parts AB, BC and CD, as shown in figure. The rod is subjected to a pull of 25 kN. Diamerter of parts AB and CD is 50 mm while diametre of port BC is 25 mm. The total extension of the rod is (Young’s modulus for steel = 2 × 10 ^{11} N m^{–2}) **

(a) 0.0637 mm

(b) 0.0647 mm

(c) 0.0657 mm

(d) 0.0667 mm

## Answer

A

**Question. The bulk modulus of water if its volume changes from 100 litre to 99.5 litre under a pressure of 100 atm is****(Take 1 atm = 10 ^{5} N m^{–2})**

(a) 2 × 10

^{7}N m

^{–2}

(b) 2 × 10

^{8}N m

^{–2}

(c) 2 × 10

^{9}N m

^{–2}

(d) 2 × 10

^{10}N m

^{–2 }

## Answer

C

**Question. The volume change of a solid copper cube 10 cm on an edge, when subjected to a pressure of 7 MPa is (Bulk modulus of copper = 140 GPa) **

(a) 5 × 10^{–2} cm^{3}

(b) 10 × 10^{–2} cm^{3}

(c) 15 × 10^{–2} cm^{3}

(d) 20 × 10^{–2} cm^{3 }

## Answer

A

**Question. The length of an iron wire is L and area of cross-section is A. The increase in length is l on applying the force F on its two ends. Which of the following statements is correct ?**

(a) Increase in length is inversely proportional to its length L.

(b) Increase in length is proportional to area of cross-section A.

(c) Increase in length is inversely proportional to cross-section A.

(d) Increase in length is proportional to Young’s modulus.

## Answer

C

**Question. A steel wire of length 4.7 m and crosssectional area 3.0 × 10 ^{–5} m^{2} stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 × 10^{–5} m^{2} under a given load. What is the ratio of the Young’s modulus of steel to that of copper?**

(a) 1.8 : 1

(b) 2.8 : 1

(c) 3.8 : 1

(d) 4.8 : 1

## Answer

A

**Question. A and B are two wires. The radius of A is twice that of B. If they are stretched by the same load, then the stress on B is **

(a) equal to that of A

(b) two times that of A

(c) four times that of A

(d) half that of A.

## Answer

C

**Question. A wire of cross-section 4 mm2 is stretched by 0.1 mm by a certain weight. How far (length) will the wire of same material and length but of area 8 mm ^{2} stretch under the action of same force?**

(a) 0.05 mm

(b) 0.10 mm

(c) 0.15 mm

(d) 0.20 mm

## Answer

A

**Question. The length of an elastic spring is a metres when a force of 4 N is applied, and b metres when the 5 N force is applied. Then the length of the spring when the 9 N force is applied is**

(a) a + b

(b) 9b – 9a

(c) 5b – 4a

(d) 4a – 5b

## Answer

C

**Question. For a perfectly rigid body**

(a) Young’s modulus is infinite and bulk modulus is zero.

(b) Young’s modulus is zero and bulk modulus is infinite.

(c) Young’s modulus is infinite and bulk modulus is also infinite.

(d) Young’s modulus is zero and bulk modulus is also zero.

## Answer

C

**Question. A wire of length L and radius r fixed at one end and a force F applied to the other end produces an extension l. The extension produced in another wire of the same material of length 2 L and radius 2r by a force 2F, is**

(a) ∫

(b) 2∫

(c) 4∫

(d) ∫/2

## Answer

A

**Question. The compressibility of water is 6 × 10 ^{–10} N^{–1}m^{2}. If one litre is subjected to a pressure of 4 × 10^{7} N m^{–2}, the decrease in its volume is**

(a) 10 cc

(b) 24 cc

(c) 15 cc

(d) 12 cc

## Answer

D

**Question. The pressure of a medium is changed from 1.01 × 10 ^{5} Pa to 1.165 × 10^{5} Pa and change in volume is 10% keeping temperature constant. **

**Find the bulk modulus of the medium.**

(a) 1 × 10

^{3}Pa

(b) 3 × 10

^{5}Pa

(c) 2 × 10

^{4}Pa

(d) 1.55 × 10

^{5}Pa

## Answer

D

**Question. How much pressure should be applied on a litre of water if it is to be compressed by 0.1%?****(Bulk modulus of water = 2100 MPa)**

(a) 2100 kPa

(b) 210 kPa

(c) 2100 MPa

(d) 210 MPa

## Answer

A

**Question. A steel cable with a radius 2 cm supports a chairlift at a ski area. If the maximum stress is not to exceed 10 ^{8} N m^{–2}, the maximum load the cable can support is**

(a) 4π × 10

^{5}N

(b) 4π × 10

^{4}N

(c) 2π × 10

^{5}N

(d) 2π × 10

^{4}N

## Answer

B

**Question. The radii and Young’s moduli of two uniform wires A and B are in the ratio 2 : 1 and 1 : 2 respectively. Both wires are subjected to the same longitudinal force. If the increase in length of the wire A is one percent, the percentage increase in length of the wire B is**

(a) 1.0

(b) 1.5

(c) 2.0

(d) 3.0

## Answer

C

**Question. Two wires of equal length and cross-section area are suspended as shown in figure. Their Young’s modulus are Y _{1} and Y_{2} respectively.**

**The equivalent Young’s modulus will be**

(a) Y_{1} + Y2

(b) Y_{1 }+ Y_{2 }/ 2

(c) Y_{1}Y_{2 }/ Y_{1 }+ Y_{2}

(d) √Y_{1} Y_{2 }

## Answer

B

**Question. The area of a cross-section of steel wire is 0.1 cm2 and Young’s modulus of steel is 2 × 10 ^{11} N m^{–2}. The force required to stretch by 0.1% of its length is**

(a) 2000 N

(b) 1000 N

(c) 1500 N

(d) 1700 N

## Answer

A

**Question. Uniform rod of mass m, length l , area of cross-section A has Young’s modulus Y. If it is hanged vertically, elongation under its own weight will be **

(a) mgl /2AY

(b) 2mgl /AY

(c) mgl /AY

(d) mgY/Al

**Answer**

C

**Question. Which one of the following affects the elasticity of a substance ? **

(a) Change in temperature

(b) Hammering and annealing

(c) Impurity in substance

(d) All of the above

**Answer**

D

**Question. According to Hooke’s law of elasticity, if stress is increased, then the ratio of stress to strain **

(a) becomes zero

(b) remains constant

(c) decreases

(d) increases

**Answer**

B

**Question. The length of an iron wire is L and area of corss-section is A. The increase in length is l on applying the force F on its two ends. Which of the statement is correct? **

(a) Increase in length is inversely proportional to its length

(b) Increase in length is proportional to area of crosssection

(c) Increase in length is inversely proportional to area of cross-section

(d) Increase in length is proportional to Young’s modulus

**Answer**

C

**Question. A and B are two wires. The radius of A is twice that of B. **

They are stretched by the same load. Then the stress on B is

(a) equal to that on A

(b) four times that on A

(c) two times that on A

(d) half that on A

**Answer**

B

**Question. Hooke’s law defines **

(a) stress

(b) strain

(c) modulus of elasticity

(d) elastic limit

**Answer**

C

**Question. In case of steel wire (or a metal wire), the limit is reached when **

(a) the wire just break

(b) the load is more than the weight of wire

(c) elongation is inversely proportional to the tension

(d) None of these

**Answer**

D

**Question. A steel ring of radius r and cross sectional area A is fitted onto a wooden disc of radius R (R > r). If the Young’s modulus of steel is Y, then the force with which the steel ring is expanded is **

(a) A Y (R/r)

(b) A Y (R – r)/r

(c) (Y/A)[(R – r)/r]

(d) Y r/A R

**Answer**

B

**Question. Which of the following relation is true ? **

(a) 3Y = K(1- σ )

(b K = 9ηY /Y+η

(c) σ = (6K + η)Y

(d) σ = 0.5Y – η / η

**Answer**

D

**Question. For a constant hydraulic stress on an object, the fractional change in the object volume (Δ V /V) and its bulk modulus (B) are related as **

(a) Δ

*V*/

*V ∝ B*

(b) Δ

*V /V ∝*1

*/B*

(c) Δ

*V*/

*V ∝ B*

(d) Δ

^{2}*V*/

*V ∝ B*

^{–2}**Answer**

B

**Question. A steel wire is suspended vertically from a rigid support. ****When loaded with a weight in air, it extends by la and when the weight is immersed completely in water, the extension is reduced to lw. Then the relative density of material of the weight is**

(a) la /lw

(b) la / la – lw

(c) lw / la – lw

(d) lw – la

**Answer**

B

**Question. When an elastic material with Young’s modulus Y is subjected to stretching stress S, elastic energy stored per unit volume of the material is **

(a) YS / 2

(b) S2Y / 2

(c) S2 / 2Y

(d) S / 2Y

**Answer**

C

**Question. The ratio of shearing stress to the corresponding shearing strain is called **

(a) bulk modulus

(b) Young’s modulus

(c) modulus of rigidity

(d) None of these

**Answer**

C

**Question. The Young’s modulus of a perfectly rigid body is **

(a) unity

(b) zero

(c) infinity

(d) some finite non-zero constant

**Answer**

C

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