CBSE Class 11 Physics Mechanical Properties Of Solids Worksheet

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)

Question- Hooke's law states that

(a) stress is directly proportional to strain

(b) stress is inversely proportional to strain

(c) stress is equal to strain

(d) stress and strain are independent of each other

Answer-(a)

Question- A 2 m long rod of radius 1 cm which is fixed from one end is given a twist of 0.8 radians. The shear strain developed will be

(a) 0.002

(b) 0.004

(c) 0.008

(d) 0.016

Answer-(b)

Question- Which of the following materials is most elastic?

(a) Steel

(b) Rubber

(c) Copper

(d) Glass

Answer-(a)

Question-The reciprocal of the bulk modulus is called

(a) modulus of rigidity

(b) volume stress

(c) volume strain

(d) compressibility

Answer-(d)

Question- What is the phenomenon of temporary delay in regaining the original configuration by an elastic body, after the removel of a deforming force?

(a) Elastic fatigue

(b) Elasticity

(c) Plasticity

(d) Elastic after effect

Answer-(d)

Question-Substances which can be stretched to cause large strains are called

(a) brittle

(b) ductile

(c) plastic

(d) elastomer

Answer-(d)

Question- If the length of a wire is reduced to half, then it can hold the

(a) half load

(b) same load

(c) double load

(d) one fourth load

Answer-(b)

Question- The reason for the change in shape of a regular body is

(a) volume stress

(b) shearing strain

(c) longitudinal strain

(d) metallic strain

Answer-(b)

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-When forces are applied on a body such that it is still in static equilibrium, then the extent to which the body gets deformed, depends on

(a) nature of the material

(b) magnitude of deforming force

(c) Both (a) & (b)

(d) None of these

Answer-(c)

Question-The correct increasing order of coefficient of elasticity of Copper, Steel, Glass and Rubber is

(a) Steel, Rubber, Copper, Glass

(b) Rubber, Copper, Glass, Steel

(c) Rubber, Glass, Steel, Copper

(d) Rubber, Glass, Copper, Steel

Answer-(d)

Question-Which of the following substance has the lowest elasticity?

(a) Steel

(b) Copper

(c) Rubber

(d) wood

Answer-(a)

Question- Which of the following is not a type of stress?

(a) Tensile stress

(b) Compressive stsress

(c) Hydraulic stress

(d) None of these

Answer-(d)

Question-In magnitude hydraulic stress is equal to 

(a) hydraulic force

(b) hydraulic pressure

(c) restoring force

(d) hydraulic strain

Answer-(b)

Question. The restoring force per unit area is known as
(a) strain
(b) elasticity
(c) stress
(d) plasticity

Answer: C

Question. Which of the following elastic moduli is used to describe the elastic behaviour of object as they respond to the deforming forces acting on them?
(a) Young's modulus
(b) Shear modulus
(c) Bulk modulus
(d) All of these

Answer: D

Question. The property of a body by virtue of which it tends to regain its original size and shape when the applied force is removed is called
(a) elasticity
(b) plasticity
(c) rigidity
(d) compressibility

Answer: A

Question. The isothermal bulk modulus of a gas at atmospheric pressure is
(a) 1 mm of Hg
(b) 13.6 mm of Hg
(c) 1.013 × 10⁵ N/m²
(d) 2.026 × 10⁵ N/m²

Answer: C

Question. The ratio of stress and strain is called
(a) elastic limit
(b) plastic deformation
(c) modulus of elasticity
(d) tensile strength

Answer: C

Question. According to Hook’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. Which of the following types of stress causes no chang in shape?
(a) Compressive stress
(b) Hydraulic stress
(c) Shearing stress
(d) None of these

Answer: B

Question. The ratio of tensile stress to the longitudinal strain is defined as
(a) modulus of elasticity
(b) Yong's modulus
(c) bulk modulus
(d) None of these

Answer: B

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 the above

Answer: D

Question. The only elastic modulus that applies to fluids is
(a) Young's modulus
(b) modulus of rigidity
(c) bulk modulus
(d) shear modulus

Answer: C

Question. If the load is increased beyond the _______ point, the strain increases rapidly for even a small change in the stress.
(a) elastic point
(b) yield point
(c) plastic point
(d) fracture point

Answer: B

Question. Shearing stress change _______ of the body.
(a) length
(b) breadth
(c) shape
(d) volume

Answer: C

Question. A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain is
(a) 0.01
(b) 0.06
(c) 0.02
(d) 0.03

Answer: D

Question. The temperature of a wire is doubled. The Young's modulus of elasticity
(a) will also double
(b) will become four times
(c) will remain same
(d) will decrease

Answer: D

Question. A spring is stretched by applying a load to its free end. The strain produced in the spring is
(a) volumetric
(b) shear
(c) longitudinal and shear
(d) longitudinal

Answer: C

Question. In Searle's experiment to find Young's modulus the diameter of wire is measured as d = 0.05cm, length of wire is l = 125cm and when a weight, m = 20.0 kg is put, extension in wire was found to be 0.100 cm. Find maximum permissible error in Young's modulus (Y). Use : Y = mgl/(π/4)d² x
(a) 6.3%
(b) 5.3%
(c) 2.3%
(d) 1%

Answer: A

Question. If the ratio of lengths, radii and Young’s modulus of steel and brass wires shown in the figure are a, b, and c, respectively. The ratio between the increase in lengths of brass and steel wires would be 

(a) b² a/2c
(b) bc/2a²
(c) ba²/2c
(d) a/2b²c

Answer: D

Question. A mild steel wire of length 2L and cross-sectional area A is stretched, well within elastic limit, horizontally between two pillars (figure ). A mass m is suspended from the mid-point of the wire. Strain in the wire is 

(a) x²/2L2
(b) x/L
(c) x²/L
(d) x²/2L

Answer: A

Question. A rectangular frame is to be suspended symmetrically by two strings of equal length on two supports (figure). It can be done in one of the following three ways; 
The tension in the strings will be
(a) the same in all cases
(b) least in (a)
(c) least in (b)
(d) least in (c)

Answer: C

Question. Which one of the following is not a unit of Young’s modulus ?
(a) Nm^–1
(b) Nm^–2
(d) dyne cm^–2
(d) mega pascal

Answer: A

Question. Consider two cylindrical rods of identical dimensions, one of rubber and the other of steel. Both the rods are fixed rigidly at one end to the roof. A mass M is attached to each of the free ends at the centre of the rods.
(a) Both the rods will elongate but there shall be no perceptible change in shape
(b) The steel rod will elongate and change shape but the rubber rod will only elongate
(c) The steel rod will elongate without any perceptible change in shape, but the rubber rod will elongate and the shape of the bottom edge will change to an ellipse
(d) The steel rod will elongate, without any perceptible change in shape, but the rubber rod will elongate with the shape of the bottom edge tapered to a tip at the centre

Answer: D

Question. When a 4 kg mass is hung vertically on a light spring that obeys Hooke’s law, the spring stretches by 2 cms. The work required to be done by an external agent in stretching this spring by 5 cms will be (g = 9.8 m/sec²)
(a) 4.900 joule
(b) 2.450 joule
(c) 0.495 joule
(d) 0.245 joule

Answer: B

Question. A rigid bar of mass M is supported symmetrically by three wires each of length l. Those at each end are of copper and the middle one is of iron. The ratio of their diameters, if each is to have the same tension, is equal to 

Answer: B

Question. A 5 metre long wire is fixed to the ceiling. A weight of 10 kg is hung at the lower end and is 1 metre above the floor. The wire was elongated by 1 mm. The energy stored in the wire due to stretching is
(a) zero
(b) 0.05 joule
(c) 100 joule
(d) 500 joule

Answer: B

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 103 kg/m³.What fractional compression of water will be obtained at the bottom of the ocean ? 
(a) 1.0 × 10^–2
(b) 1.2 × 10^–2
(c) 1.4 × 10^–2
(d) 0.8 × 10^–2

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 = 100 cm, diameter = 1 mm
(b) Length = 200 cm, diameter = 2 mm
(c) Length = 300 cm, diameter = 3 mm
(d) Length = 50 cm, diameter = 0.5 mm

Answer: D

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) Δl versus 1/l
(b) Δl versus l²
(c) Δl versus 1/l²
(d) Δl versus l 

Answer: B

Question. Modulus of rigidity of a liquid is
(a) constant
(b) infinite
(c) zero
(d) cannot be predicted

Answer: C

Question. Shearing strain is expressed by
(a) angle of shear
(b) angle of twist
(c) decrease in volume
(d) increase in volume

Answer: A

DIRECTIONS for : type questions. Each of these question contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Answer these questions from the following four options.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement -1
(b) Statement-1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement - 1
(c) Statement-1 is True, Statement- 2 is False
(d) Statement-1 is False, Statement -2 is True

Question. Statement 1 : The stress-strain graphs are shown in the figure for two materials A and B are shown in figure. Young's modulus of A is greater than that of B. 

Statement 2 : The Young's modules for small strain is, Y = stress/strain = slope of linear portion, of graph; and slope of A is more than slope that of B.

Answer: D

Question. Statement 1: Young’s modulus for a perfectly plastic body is zero.
Statement 2: For a perfectly plastic body, restoring force is zero.

Answer: D

Question. Statement 1: Strain causes the stress in an elastic body.
Statement 2: An elastic rubber is more plastic in nature.

Answer: A

Question. Statement-1 Identical springs of steel and copper are equally stretched. More work will be done on the steel spring.
Statement-2 Steel is more elastic than copper.

Answer: A

Question. Statement-1 Stress is the internal force per unit area of a body.
Statement-2 Rubber is less elastic than steel.

Answer: B

Question. Which of the following has no dimensions ?
(a) strain
(b) angular velocity
(c) momentum
(d) angular momentum

Answer: A

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. Two rods A and B of the same material and length have their radii r₁ and r₂ respectively. When they are rigidly fixed at one end and twisted by the same couple applied at the other end, the ratio (Angle of twist at the end of A/Angle of twist at the end of B) is
(a) r₁²/r₂²
(b) r₁³/r₂³
(c) r₂⁴/r₁⁴
(d) r₁⁴/r24

Answer: C

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. 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. 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. The load versus elongation graph for four wires is shown. The thinnest wire is 

(a) P
(b) Q
(c) R
(d) S

Answer: B

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. Hooke's law defines
(a) stress
(b) strain
(c) modulus of elasticity
(d) elastic limit

Answer: C

Question. The upper end of a wire of diameter 12mm and length 1m is clamped and its other end is twisted through an angle of 30°. The angle of shear is
(a) 18°
(b) 0.18°
(c) 36°
(d) 0.36°

Answer: B

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. For a constant hydraulic stress on an object, the fractional change in the object volume (ΔV/V) and its bulk modulus (B) are related as
(a) ΔV/V ∝ B
(b) ΔV/V ∝ 1/B
(c) ΔV/V ∝ B²
(d) ΔV/V ∝ B^-2

Answer: B

Question. The diagram shown below represents the applied forces per unit area with the corresponding change X (per unit length) produced in a thin wire of uniform cross section in the curve shown. The region in which the wire behaves like a liquid is 

(a) ab
(b) bc
(c) cd
(d) Oa

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 l_w. Then the relative density of material of the weight is
(a) l _a / lw
(b) l_a/l_a - l_w
(c) l_w /(l _a - l_w )
(d) l_w / l_a

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 potential energy U between two atoms in a diatomic molecules as a function of the distance x between atoms has been shown in the figure. The atoms are 

(a) attracted when x lies between A and B and are repelled when x lies between B and C
(b) attracted when x lies between B and C and are repelled when x lies between A and B
(c) are attracted when they reach B from C
(d) are repelled when they reach B from A

Answer: B

Question. A metalic rod of length l and cross-sectional area A is made of a material of Young modulus Y. If the rod is elongated by an amount y, then the work done is proportional to
(a) y
(b) 1/y
(c) y²
(d) 1/y²

Answer: C

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 = 100 cm, diameter = 1 mm
(b) Length = 200 cm, diameter = 2 mm
(c) Length = 300 cm, diameter = 3 mm
(d) Length = 50 cm, diameter = 0.5 mm

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: 

Question. A body of mass 10 kg is attached to a wire of radius 3 cm. It’s breaking stress is 4.8 × 10⁷ Nm^–2, the area of cross-section of the wire is 10^–6 m². 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. A cube is subjected to a uniform volume compression. If the side of the cube decreases by 2% the bulk strain is
(a) 0.02
(b) 0.03
(c) 0.04
(d) 0.06

Answer: D

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 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. 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. A metal rod of Young's modulus 2 × 10¹⁰ N m^–2 undergoes an elastic strain of 0.06%. The energy per unit volume stored in J m^–3 is
(a) 3600
(b) 7200
(c) 10800
(d) 14400

Answer: A

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 cross-sectional area 3A. If the length of wire 1 increases by Dx on applying force F, how much force is needed to stretch wire 2 by the same amount?
(a) 4 F
(b) 6 F
(c) 9 F
(d) F

Answer: C

Question. A force of 10³ newton, stretches the length of a hanging wire by 1 millimetre. The force required to stretch a wire of same material and length but having four times the diameter by 1 millimetre is
(a) 4 × 10³ N
(b) 16 × 10³ N
(c) 1/4 x 10³ N
(d) 1/16 x 10³ N

Answer: B

Question. A 2 m long rod of radius 1 cm which is fixed from one end is given a twist of 0.8 radian. The shear strain developed will be
(a) 0.002
(b) 0.004
(c) 0.008
(d) 0.016

Answer: B

Question. To break a wire, a force of 106 N/m2 is required. If the density of the material is 3 × 103 kg/m3, then the length of the wire which will break by its own weight will be
(a) 34 m
(b) 30 m
(c) 300 m
(d) 3 m

Answer: A

Question. There are two wire of same material and same length while the diameter of second wire is two times the diameter of first wire, then the ratio of extension produced in the wires by applying same load will be
(a) 1 : 1
(b) 2 : 1
(c) 1 : 2
(d) 4 : 1

Answer: D

Question. A cube at temperature 0ºC is compressed equally from all sides by an external pressure P. By what amount should its temperature be raised to bring it back to the size it had before the external pressure was applied. The bulk modulus of the material of the cube is B and the coefficient of linear expansion is a.
(a) P/B α
(b) P/3 B α
(c) 3 π α/B
(d) 3 B/P

Answer: B

Question. The compressibility of water is 4 × 10^–5 per unit atmospheric pressure. The decrease in volume of 100 cm³ of water under a pressure of 100 atmosphere will be
(a) 0.4 cm³
(b) 4 × 10^–5 cm³
(c) 0.025 cm³
(d) 0.004 cm³

Answer: A

Question. For the same cross-sectional area and for a given load, the ratio of depressions for the beam of a square cross-section and circular cross-section is
(a) 3 : π
(b) π : 3
(c) 1 : π
(d) π : 1

Answer: A

Question. A massive stone pillar 20 m high and of uniform crosssection rests on a rigid base and supports a vertical load of 5.0 × 10⁵ N at its upper end. If the compressive stress in the pillar is not to exceed 1.6 × 10⁶ N m^–2, what is the minimum cross-sectional area of the pillar? Density of the stone = 2.5 × 10³ kg m^–3. (Take g = 10 N kg^–1)
(a) 0.15 m²
(b) 0.25 m²
(c) 0.35 m²
(d) 0.45 m²

Answer: D

Question. The length of a metal is l₁ when the tension in it is T₁ and is l₂ when the tension is T₂. The original length of the wire is
(a) l₁+l₂/2
(b) l₁T+l₂T/T₁+T₂
(c) l₁T₂ - l₂T₁/T₁-T₂
(d) √T₁T₂l₁l₂

Answer: C

Question. From a steel wire of density r is suspended a brass block of density ρ_b. The extension of steel wire comes to e. If the brass block is now fully immersed in a liquid of density ρ_l, the extension becomes e'. The ratio e/e' will be
(a) ρb/ρb - ρl
(b) ρb - ρl/ρb
(c) ρb - ρ/ρl - ρ
(d) ρl/ρb - ρl

Answer: A

Question. One end of a uniform wire of length L and of weight W is attached rigidly to a point in the roof and W₁ weight is suspended from looser end. If A is area of cross-section of the wire, the stress in the wire at a height L/4 from the upper end is
(a) W₁ +W/a
(b) W₁ + 3W/ 4/a
(c) W W/4/a
(d) 4W₁ + 3W/a

Answer: B