Elastic behaviour, stress-strain, Hooke's law, Young's, bulk and rigidity moduli
- The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young's modulus, respectively, are 8×10^8 N m^-2 and 2×10^11 N m^-2, is : Answer: 2. 4 mm Key idea: The largest stress the wire can bear without permanent change is the elastic limit. Use Y=stress/strain . Strain =... 1
- Let a wire be suspended from the ceiling (rigid support) and stretched by a weight W attached at its free end. The longitudinal stress at any point of cross-sectional area A of the wire is : Answer: 3. W/A The wire is in equilibrium under the weight W at the free end (the wire's own weight is neglected). The tension at every cros... 1
- Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).Assertion (A) : The stretching of a spring is determined by the shear modulus of the material of the spring.Reason (R) : A coil spring of copper… Answer: 4. (A) is true but (R) is false Assertion: when a spring is stretched, the wire of the coil is mainly twisted, which is a shear defo... 1
- A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changes to L_1 when mass M is suspended from its free end. The expression for Young's modulus is : Answer: 4. MgL/A(L₁ - L) Young's modulus Y=stress/strain . Stress =Mg/A Strain =L₁-L/L , since the extension is L₁-L and the original length... 1
- When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L+l). The elastic potential energy stored in the extended wire is : Answer: 3. 1/2Mgl The energy stored in a stretched wire equals the work done by the stretching force, which grows linearly from 0 to Mg . U=... 1
- Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by Δ l on applying a force F, how much force is… Answer: 1. 9 F Same volume: A l=3A l₂ , so the second wire has length l₂=l/3 . From Y=F l/A Δ l , F=YAΔ l/l . F₂=Y(3A)Δ l/l/3=9·YAΔ l/l=9F 1
- The bulk modulus of a spherical object is 'B'. If it is subjected to uniform pressure 'p', the fractional decrease in radius is : Answer: 3. p/3B Key idea: B=p/Δ V/V , and for a sphere V∝ r³ , so Δ V/V=3Δ r/r . Δ r/r=1/3Δ V/V=p/3B . 1