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NCERT Solutions for class 11 Physics | Chapter 9 - Mechanical Properties of Solids

(1) A copper and a steel wire of the same diameter are connected end to end. A deforming force F is applied to this composite wire which causes a total elongation of 1 cm. The two wires will have
[A] the same stress
[B] different stress
[C] the same strain
[D] different strain
Answer: A, D
(2) For an ideal liquid
[A] the bulk modulus is infinite
[B] the bulk modulus is zero
[C] the shear modulus is infinite
[D] the shear modulus is zero
Answer: A, D

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(3) A wire is suspended from the ceiling and stretched under the action of a weight F suspended from its other end. The force exerted by the ceiling on it is equal and opposite to the weight.
[A] tensile stress at any cross-section A of the wire is F/A
[B] tensile stress at any cross-section is zero
[C] tensile stress at any cross-section A of the wire is 2F/A
[D] tension at any cross-section A of the wire is F
Answer: A, D
(4) The stress-strain graphs for the two materials are shown in the figure.
[A] material (ii) is more elastic than material (i) and hence material (ii) is more brittle
[B] material (i) and (ii) have the same elasticity and the same brittleness
[C] material (ii) is elastic over a larger region of strain as compared to (i)
[D] material (ii) is more brittle than material (i)
Answer: C, D
(5) 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: 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
(6) 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: longitudinal and shear
(7) 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: will decrease
(8) The maximum load a wire can withstand without breaking when its length is reduced to half of its original length, will
[A] be doubled
[B] be half
[C] be four times
[D] remain same
Answer: remain same
(9) Modulus of rigidity of ideal liquid is
[A] infinity
[B] zero
[C] unity
[D] some finite small non-zero constant value
Answer: zero
(10) A copper and a steel wire of the same diameter are connected end to end. A deforming force F is applied to this composite wire which causes a total elongation of 1cm. The two wires will have
[A] the same stress.
[B] different stress.
[C] the same strain.
[D] different strain.
Answer: A, D
(11) 9A rod of length l and negligible mass is suspended at its two ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths (Fig. in below). The cross-sectional areas of wires A and B are 1.0 mm2 and 2.0 mm2, respectively.
(YAl 70 * 109 Nm– 2 and Ysteel 200 * 109 Nm-2

[A] Mass m should be suspended close to wire A to have equal stresses in both the wires.
[B] Mass m should be suspended close to B to have equal stresses in both the wires.
[C] Mass m should be suspended at the middle of the wires to have equal stresses in both the wires.
[D] Mass m should be suspended close to wire A to have equal strain in both wires.
Answer: B, D
(12) The stress-strain graphs for two materials are shown in Fig. below (assume same scale)

[A] Material (ii) is more elastic than material (i) and hence material (ii) is more brittle.
[B] Material (i) and (ii) have the same elasticity and the same brittleness.
[C] Material (ii) is elastic over a larger region of strain as compared to (i).
[D] Material (ii) is more brittle than material (i).
Answer: C, D
(13) A rectangular frame is to be suspended symmetrically by two strings of equal length on two supports (Fig. in below). 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: least in (b).
(14) A mild steel wire of length 2L and cross-sectional area A is stretched, well within elastic limit, horizontally between two pillars (Fig. in below). A mass m is suspended from the mid point of the wire. Strain in the wire is

[A] x2 / 2 L2
[B] x / L
[C] x2 / L
[D] x22 / 2 L
Answer: x2 / 2 L2
(15) 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

[A] (a)
[B] (b)
[C] (c)
[D] (d)
Answer: (b)
(16) 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: remain same.
(17) Modulus of rigidity of ideal liquids is
[A] infinity.
[B] zero.
[C] unity.
[D] some finite small non-zero constant value.
Answer: zero
(18) Streamline flow is more likely for liquids with
[A] low density and high viscosity
[B] low density and high viscosity
[C] high density and high viscosity
[D] high density and high viscosity
Answer: low density and high viscosity
(19) The Poisson’s ratio of a material is 0.5. If a force is applied to a wire of this material, there is a decrease in the cross-sectional area by 4%. The percentage increase in the length is
[A] 4%
[B] 2.5%
[C] 2%
[D] 1%
Answer: 4%
(20) In Bernoulli’s theorem which of the following is conserved?
[A] Energy
[B] Mass
[C] Linear momentum
[D] Angular momentum
Answer: Energy

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