CBSE Class 11 Physics Mechanical Properties of Solids MCQs Set D

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

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 steel wire of length 20 cm and uniform cross-section 1 mm2 is tied rigidly at both the ends. The temperature of the wire is altered from 40ºC to 20ºC. Coefficient of linear expansion for steel a = 1.1 × 10^–5/ºC and Y for steel is 2.0 × 10¹¹ N/m². The change in tension of the wire is
(a) 2.2 × 10⁶ newton
(b) 16 newton
(c) 8 newton
(d) 44 newton
Answer: d

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. 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. 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. The Young’s modulus of brass and steel are respectively 10¹0 N/m². and 2 × 10¹⁰ N/m². 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 R_B and R_S 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. For a given material, the Young’s modulus is 2. 4 times that of rigidity modulus. Its Poisson’s ratio is
(a) 2.4
(b) 1.2
(c) 0.4
(d) 0.2
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 a
(b) P/3 B a
(c) 3 π a/B
(d) 3 B/P
Answer: b

Question. On stretching a wire, the elastic energy stored per unit volume is
(a) Fl/2AL
(b) FA/2L
(c) FL/2A
(d) FL/2
Answer: a

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/cm² is
(a) 10 × 10¹²
(b) 100 × 10¹²
(c) 1 × 10¹²
(d) 10 × 10¹²
Answer: c

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. What per cent of length of wire increases by applying a stress of 1 kg weight/mm2 on it? (Y = 1 × 10¹¹ N/m² and 1 kg weight = 9.8 newton)
(a) 0.0067%
(b) 0.0098%
(c) 0.0088%
(d) 0.0078%
Answer: b

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. A material has poisson’s ratio 0.50. If a uniform rod of it suffers a longitudinal strain of 2 × 10^–3, then the percentage change in volume is
(a) 0.6
(b) 0.4
(c) 0.2
(d) Zero
Answer: d

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. 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. Two wires A and B are of the same material. Their lengths are in the ratio of 1 : 2 and the diameter are in the ratio 2 : 1. If they are pulled by the same force, then increase in length will be in the ratio of
(a) 2 : 1
(b) 1 : 4
(c) 1 : 8
(d) 8 : 1
Answer: c

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 Δx 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 rod of length l and radius r is joined to a rod of length l/2 and radius r/2 of same material. The free end of small rod is fixed to a rigid base and the free end of larger rod is given a twist of q°, the twist angle at the joint will be
(a) θ/4
(b) θ/2
(c) 5θ/6
(d) 8θ/48
Answer: d

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 : 2
Y = mgl/(π /4) d² x
(a) 6.3%
(b) 5.3%
(c) 2.3%
(d) 1%
Answer: a

Question. The maximum load a wire can withstand without breaking, when its length is reduced to half of its original length, will
(a) be double
(b) be half
(c) be four times
(d) remain same
Answer: d

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. 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. Modulus of rigidity of ideal liquids is
(a) infinity
(b) zero
(c) unity
(d) some finite small non-zero constant value
Answer: b

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. 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 ‘Δl’. 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. 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. 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. 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. 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