Class 11 Physics, Chapter 8 (NCERT). 15 questions by concept, 2 with pictures. Open “Show answer” for the answer and why.
How to teach this chapter · Common misconceptions & worked visual for this chapter
A straight wire is pulled by equal opposite forces of 200 N at its two ends and is in equilibrium. Its area is 5 mm². What tensile stress is present?
(a) 40 MPa
A cross-section transmits one end load F, although the whole wire has zero resultant. Stress = F/A; one N/mm² equals one MPa.
A wire of area 2 mm² has tensile stress 80 MPa under equal opposite end pulls. What is the magnitude of each end pull?
(c) 160 N
Stress is tension divided by cross-sectional area, using one end pull. Thus each pull is σA; do not split that value between the two ends.
A wire originally 500 mm long and 4 mm in diameter lengthens by 1 mm while its diameter contracts by 3/1250 mm. What is Poisson ratio, using contraction as a positive magnitude?
(c) 3/10
Normalize lateral contraction by original diameter, and extension by original length. Poisson ratio compares these two strains, not the absolute changes.
A wire of original length 1000 mm and diameter 2 mm extends by 1 mm. Its Poisson ratio is 3/10. What is the magnitude of its diameter contraction?
(c) 3/5000 mm
Lateral contraction strain is ν times longitudinal strain ΔL/L. Multiply that lateral strain by the original diameter to obtain its contraction.
A total load of 40000 N is shared equally by 4 identical vertical columns. Each column has length 2 m, area 100 mm² and Y = 200 GPa. What is the shortening of each column in the linear regime?
(c) 1 mm
Each column carries F_total/4, not the full load. Use compression FL/(AY) for that individual load.
Each of 2 identical parallel supports has area 50 mm², Young modulus 100 GPa and compressive-strain magnitude 1/500. They share the structure load equally. What total load do they support?
(a) 20000 N
Each support carries YAε, converting GPa to N/mm² by multiplying by 1000. The total supported load is 2 times the individual load.
Two circular wires have the same material, length and tensile load. Wire B has 3 times wire A’s diameter. What is elongation(B)/elongation(A) in the linear regime?
(c) 1/9
Cross-sectional area is proportional to diameter squared. Elongation FL/(AY) is inversely proportional to area.
At fixed material, length and load, a new circular wire must have 1/4 of the old wire’s elongation. What is new diameter/old diameter?
(b) 2
The new area must be 4 times the old area. Diameter scales as the square root of area, not linearly with it.
The graph shows the proportional region of a material’s stress-strain response. What is its Young modulus?
(c) 100 GPa
The horizontal labels represent strain multiplied by 10^-3, while stress is in MPa. Divide stress by strain: the endpoint gives 400 MPa/0.004 = 100 GPa.
The two material curves use the same stress and strain scales. Which statement correctly compares initial Young modulus and ultimate tensile strength?
(c) B has the greater Young modulus; A has the greater ultimate strength.
Initial stress-strain slope determines Young modulus; maximum stress determines ultimate strength. The steeper initial curve and the higher peak belong to different materials.
One face of a solid is fixed. A tangential force of 900 N acts on the opposite face of area 1/20 m², separated by 1/2 m. Its shear modulus is 28/5 GPa and Young modulus is 16 GPa. What is the face displacement in micrometres in the small-strain regime?
(b) 45/28 μm
Tangential displacement is a shear deformation, so use G. Δx = FL/(AG); converting GPa and metres gives the stated micrometre expression.
A specimen of original volume 1000 cm³ has bulk modulus 11/5 GPa. Its uniform pressure is increased by 11/5 MPa. What is signed ΔV = final volume − original volume in the linear approximation?
(b) -1 cm³
Bulk modulus is −Δp/(ΔV/V0), so positive Δp gives negative ΔV. Convert MPa/GPa by a factor of 1/1000 before multiplying by original volume.
An initially unstretched Hookean wire is loaded gradually from zero to 200 N and extends by 2 mm. What elastic energy is stored?
(a) 1/5 J
The force rises linearly from zero, so the average loading force is F/2. Multiply that average by the extension in metres: U = FΔL/2.
A test of a specimen of elastic tissue reaches strain 0.50 along a curved stress-strain path, then recovers its original dimensions completely when unloaded. What type of deformation is this?
(c) Elastic, but not Hookean over the full loading range.
Elasticity is established by recovery on unloading. A curved loading relation does not obey proportionality throughout, but need not leave permanent strain.
For a rectangular beam supported at its ends and loaded at the centre, sag is δ = Wl³/(4bd³Y). Keeping W, l, b and Y fixed, depth d is multiplied by 2. What is new sag/old sag?
(c) 1/8
The specified formula has depth cubed in its denominator. Thus the sag changes by the reciprocal cube of the depth factor.
Wrong
Rubber has a larger Young’s modulus than steel because it stretches easily.
Why it feels right. Everyday “elastic” means stretchy.
Right
A larger Young’s modulus means greater stiffness in the linear elastic range.
Worked example
