Free Physics of Solids MCQs with Answers

231. Why the spring is made of steel in comparison of copper

• A. Copper is more costly than steel
• B. Copper is more elastic than steel
• C. Steel is more elastic than copper
• D. None of the above

Explanation: The primary reason for using steel over copper in making springs is steel's superior elasticity. Elasticity is a material's ability to deform under stress and return to its original shape when the stress is removed. Steel, due to its higher elastic limit, is better suited for applications like springs, where repeated deformation and recovery are necessary. Copper, while a good conductor and relatively ductile, does not match steel's elasticity, making it less appropriate for this application. While cost may be a consideration, it is not the determining factor in this context. Hence, option C is correct, and options A, B, and D are incorrect for the reasons stated.

232. The ratio of diameters of two wires of the same material is n:1. The length of each wire is 4 m. On applying the same load, the increase in length of thin wire will be

• A. n2 times
• B. nt times
• C. 2n times
• D. None of the above

Explanation: When a load is applied to a wire, the elongation is given by the formula ΔL = (F × L) / (A × Y), where F is the force, L is the original length, A is the cross-sectional area, and Y is the Young's modulus of the material. Since the wires are made of the same material and under the same load, Y and F are constant. The cross-sectional area A is proportional to the square of the diameter. Therefore, if the diameter of the thin wire is 1/n times the diameter of the thicker wire, its area will be (1/n2) times smaller, leading to an elongation that is n2 times greater. Thus, the correct answer is n2 times. The other options are incorrect as they do not accurately reflect the relationship between diameter and elongation.

233. Two identical wires of rubber and iron are stretched by the same weight, then the number of atoms in the iron wire will be

• A. Equal to that of rubber
• B. Less than that of the rubber
• C. More than that of the rubber
• D. None of the above

Explanation: When identical wires of rubber and iron are stretched by the same weight, the number of atoms in the iron wire will be more than that in the rubber wire. This is due to the higher atomic density of iron compared to rubber. Iron is a metal with closely packed atoms, while rubber is a polymer with more space between its molecules. Hence, even when both wires are of the same dimensions, the iron wire contains more atoms. Option A is incorrect because it assumes the atomic density of rubber and iron to be the same, which is not true. Option B is incorrect as it wrongly assumes iron to be less dense than rubber. Option D is incorrect because it dismisses the correct option, which addresses the material properties accurately.

234. The force constant of a wire does not depend on

• A. Nature of the material
• B. Radius of the wire
• C. Length of the wire
• D. None of the above

Explanation: The force constant of a wire is influenced by the nature of the material, the radius of the wire, and its length. The material determines the intrinsic elastic properties of the wire. The radius affects the cross-sectional area, which in turn affects the stiffness, while the length influences how much the wire can stretch. Therefore, all these factors play a role in determining the force constant of the wire. The correct answer is 'None of the above' because each option lists a factor that does affect the force constant.

235. The longitudinal strain is only possible in

• A. Gases
• B. Fluids
• C. Solids
• D. Liquids

Explanation: Longitudinal strain is a type of deformation that occurs when a solid is stretched or compressed along its length. Solids can maintain their shape under force and thus can support longitudinal strain. In contrast, gases and liquids (collectively known as fluids) do not have a definite shape and cannot support this kind of strain. Gases expand to fill their container, and liquids take the shape of the container they are in, making them incapable of exhibiting longitudinal strain.

236. If the density of the material increases, the value of Young's modulus

• A. Increases
• B. Decreases
• C. First increases then decreases
• D. First decreases then increases

Explanation: Young's modulus is a measure of the stiffness of a solid material. It is defined as the ratio of stress (force per unit area) to strain (proportional deformation) in a material in the linear elasticity regime of a uniaxial deformation. Generally, in many solid materials, an increase in density is associated with a stronger atomic or molecular structure, which means that the material can withstand more stress without deforming, thus increasing Young's modulus. Therefore, the correct answer is that Young's modulus increases with an increase in density. The other options, suggesting a decrease or a non-linear relationship, are not typically observed in the majority of solid materials.

237. If Young's modulus for a material is zero, then the state of material should be

• A. Solid
• B. Solid but powder
• C. Gas
• D. None of the above

Explanation: Young's modulus measures a material's stiffness, or its ability to resist deformation. A material with a zero Young's modulus does not resist deformation at all, which is characteristic of gases. Solids and powders, even though they can be broken down into smaller particles, still possess some resistance to deformation, which means they cannot have a zero Young's modulus. Therefore, the correct answer is 'Gas', as gases can easily change shape and volume without resistance.

238. Which of the following statements is correct

• A. Hooke's law is applicable only within the elastic limit
• B. The adiabatic and isothermal elastic constants of a gas are equal
• C. Young's modulus is dimensionless
• D. Can't be predicted

Explanation: Option A is correct because Hooke's law is valid only within the elastic limit of a material, meaning the material will return to its original shape once the force is removed. Option B is incorrect because adiabatic and isothermal elastic constants differ due to different conditions of heat exchange. Option C is incorrect because Young's modulus is a measure of stiffness and has units of pressure (N/m²). Option D is incorrect as these properties can indeed be predicted based on physical principles.

239. The breaking stress of a wire depends upon

• A. Length of the wire
• B. Radius of the wire
• C. Material of the wire
• D. Shape of the cross section

Explanation: The breaking stress of a wire is a measure of the maximum stress that the material can withstand before failure. It is an intrinsic property of the material, determined by its molecular structure and bonding. Therefore, it depends on the material of the wire. The other factors, such as the length, radius, and shape of the cross-section, influence the load-bearing capacity and stress distribution but do not affect the breaking stress itself.

240. A wire of diameter 1mm breaks under a tension of 1000 N. Another wire, of same material as that of the first one, but of diameter 2 mm breaks under a tension of

• A. 500 N
• B. 1000 N
• C. 10000 N
• D. 4000 N

Explanation: The breaking tension of a wire is proportional to its cross-sectional area, which for a circular wire is given by the formula: Area = π(d/2)2. When the diameter of the wire doubles from 1 mm to 2 mm, the cross-sectional area increases by a factor of four (since (2/1)2 = 4). Therefore, the tension required to break the second wire is four times that of the first wire, resulting in a breaking tension of 4000 N. Option A (500 N) is incorrect because it incorrectly assumes a linear relationship with diameter. Option B (1000 N) is incorrect because it suggests no change in tension with increased diameter. Option C (10000 N) is incorrect because it overestimates the increase by assuming a linear relationship with area.