Free Physics of Solids MCQs with Answers

81. Dimension of modulus of elasticity

• A. [MLT^ -2]
• B. [ML^-1T^-2]
• C. [MLA-1T^21
• D. [M^-2L^-2T^-1]

Explanation: The modulus of elasticity is defined as the ratio of stress to strain.* Stress is defined as force per unit area, with dimensions (ML^-1T^-2),* Strain is dimensionless, being the ratio of change in length to the original length.Therefore, the dimension of modulus of elasticity, being the ratio of stress (with dimensions [ML^-1T^ -2]) to strain (dimensionless), inherits the dimensions of stress, which are [ML^-1T^-2]

82. In a capillary tube, water rises to a height of 4 cm. If the cross-sectional area of the tube were one-fourth, water would have risen to a height of :

• A. 2 cm
• B. 4 cm
• C. 8 cm
• D. 16 cm

Explanation: The height (h) of capillary rise is inversely proportional to the tube's radius (r). Since area (A) is proportional to r², theradius is proportional to the square root of the area. If the area becomes one-fourth, the radius is halved, causing the height to double to 8 cm.

83. A wire has tensile strain one and it is cut into half,then strain of each part is:

• A. 1
• B. 2
• C. 5
• D. 1/2

Explanation: The tensile strain remains the same because it is defined asthe ratio of change in length to the original length, which is aproperty of the material and it is independent of its length.

84. Which of the following is brittle:

• A. Glass
• B. Copper
• C. Aluminium
• D. All of these

Explanation: Glass is a non metallic material which shatters easily, makingit a classic example of a brittle material.

85. A gas undergoes a process in which the pressure and volume are related by VPn= constant. The bulk modulus of the gas is:

• A. n
• B. p1/n
• C. p/n
• D. pn

Explanation: The bulk modulus is defined as K = -V(dP/dV). By differentiating the given relation V Pⁿ = constant, we find that the bulk modulus for this specific process is K=P.n.

86. Two wires are made of the same material and have the same volume. However, wire 1 has a cross-sectional area of A, and wire 2 has a cross-sectional area of 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. F
• B. 4F
• C. 6F
• D. 9F

Explanation: Force to stretch a wire: F=YAΔL/L. Both wires have the same volume: F'/F = A'/A x L/L' = 3x3 F' = 9F

87. A ball falling in a lake of 200 m shows a decrease of 0.1% in its volume. The bulk modulus of elasticity of the material of the ball is: (take g = 10 m/s²)

• A. 10⁹ N/m²
• B. 2 × 10⁹ N/m²
• C. 3 × 10⁹ N/m²
• D. 4 × 10⁹ N/m²

Explanation: Bulk modulus is K = -ΔP / (ΔV/V). The pressure change at200 m is ΔP = ρgh = 1000×10×200 = 2 x 10⁶ Pa. The volumestrain ΔV/V is -0.1% or -0.001. Thus, K = (2 x 10⁶) / 0.001 = 2 x10⁹ N/m².

88. The rubber cord of a catapult has a cross-sectional area of 1 mm² and a total unstretched length of 10 cm. It is stretched to 12 cm and then released to project a stone of mass 5 g. Taking Young's modulus Y of rubber as 5 × 10⁸ N/m², the velocity of projection will be:

• A. 20 cm/s
• B. 20 m/s
• C. 2 m/s
• D. None of these

Explanation: The potential energy stored in the stretched cord is E = (1/2)× Stress × Strain × Volume. This stored energy is convertedinto the stone's kinetic energy (1/2)mv². Solving this energybalance equation for velocity gives 20 m/s.

89. A uniform cube is subjected to volume compression. If each side is decreased by 1.5%, then the bulk strain is:

• A. 0.045
• B. 0.03
• C. 0.45
• D. 4.5

Explanation: For small changes, the bulk strain (ΔV/V) is approximatelythree times the linear strain (ΔL/L). Since each sidedecreases by 1.5% (or 0.015), the total bulk strain isapproximately 3 × 0.015 = 0.045.

90. A vessel contains oil (density = 0.8 g/cm³) over mercury (density = 13.6 g/cm³). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere (in g/cm³) is:

• A. 3.3
• B. 6.4
• C. 7.2
• D. 12.8

Explanation: The density of the sphere is the average of the two fluiddensities, since it is half-immersed in eachρ=0.8+13.6/2 = 7.2 g/cm³.