CBSE Class 11 Physics Mechanical Properties of Solids MCQs Set 03

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 RB and RS respectively. Then
a) RS = √2 RB
b) RS = RB /√2
c) RS = 4RB
d) RS = RB / 4
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 × 1011 N m^–2)

a) 0.0637 mm
b) 0.0647 mm
c) 0.0657 mm
d) 0.0667 mm
Answer: a

Question: Hooke’s law defines
a) stress
b) strain
c) modulus of elasticity
d) elastic limit
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: 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: 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 × 108 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 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 mm2 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 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: 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 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: The compressibility of water is 6 × 10^–10 N^–1m². If one litre is subjected to a pressure of 4 × 10⁷ N m^–2, the decrease in its volume is
a) 10 cc
b) 24 cc
c) 15 cc
d) 12 cc
Answer: d

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: Which of the following has no dimensions ?
a) strain
b) angular velocity
c) momentum
d) angular momentum
Answer: a

Question: The pressure of a medium is changed from 1.01 × 10⁵ Pa to 1.165 × 10⁵ Pa and change in volume is 10% keeping temperature constant.
Find the bulk modulus of the medium.
a) 1 × 10³ Pa
b) 3 × 10⁵ Pa
c) 2 × 10⁴ Pa
d) 1.55 × 10⁵ Pa
Answer: d

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: 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 the options
Answer: d

Question: Two wires of equal length and cross-section area are suspended as shown in figure. Their Young’s modulus are Y₁ and Y₂ respectively.
The equivalent Young’s modulus will be

a) Y₁ + Y₂ 
b) Y₁ + Y₂ / 2
c) Y_1Y2  / Y₁ + Y₂ 
d) √Y_1Y2
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: 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: 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 108 N m^–2, the maximum load the cable can support is
a) 4π × 10⁵ N
b) 4π × 10⁴ N
c) 2π × 10⁵ N
d) 2π × 10⁴ N
Answer: b

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: 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: 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: The area of a cross-section of steel wire is 0.1 cm2 and Young’s modulus of steel is 2 × 1011 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: 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 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 m² stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 × 10^–5 m² 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: 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