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Mechanical Properties of Solids — NEET Physics PYQ MCQs with Solutions
Free NEET Physics PYQ Mechanical Properties of Solids MCQs with step-by-step solutions covering Stress, Strain and Hooke's Laws, Stress-Strain Curve, Thermal Stress and Elastic PE. Practise online on Prepizo — no login needed.
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Sample questions with solutions
Q1 — Stress, Strain and Hooke's Laws · medium · numerical
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
A. $\dfrac{Mg(L_1-L)}{AL}$
B. $\dfrac{MgL}{AL_1}$
C. $\dfrac{MgL}{A(L_1-L)}$ ✓ Correct
D. $\dfrac{MgL_1}{AL}$
Solution: $Y=\dfrac{F/A}{\Delta L/L}=\dfrac{Mg/A}{(L_1-L)/L}=\dfrac{MgL}{A(L_1-L)}$.
Q2 — Stress, Strain and Hooke's Laws · medium · numerical
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 $\Delta l$ on applying force $F$, how much force is needed to stretch the second wire by the same amount?
A. $4F$
B. $6F$
C. $9F$ ✓ Correct
D. $F$
Solution: Same material and volume, so $l=V/A$ and $Y=\dfrac{Fl}{A\Delta l}=\dfrac{FV}{A^2\Delta l}$ is the same for both. Hence $\dfrac{F_1}{F_2}=\dfrac{A_1^2}{A_2^2}=\dfrac{A^2}{9A^2}=\dfrac{1}{9}$, giving $F_2=9F$.
Q3 — Stress, Strain and Hooke's Laws · medium · numerical
The bulk modulus of a spherical object is $B$. If it is subjected to uniform pressure $p$, the fractional decrease in radius is
A. $\dfrac{p}{B}$
B. $\dfrac{B}{3p}$
C. $\dfrac{3p}{B}$
D. $\dfrac{p}{3B}$ ✓ Correct
Solution: $B=\dfrac{p}{\Delta V/V}$ so $\dfrac{\Delta V}{V}=\dfrac{p}{B}$. For a sphere $\dfrac{\Delta V}{V}=3\dfrac{\Delta R}{R}$, hence $\dfrac{\Delta R}{R}=\dfrac{p}{3B}$.
Q4 — Stress, Strain and Hooke's Laws · medium · numerical
Copper of fixed volume $V$ is drawn into a wire of length $l$. When this wire is subjected to a constant force $F$, the extension produced in the wire is $\Delta l$. Which of the following graphs is a straight line?
A. $\Delta l$ versus $\dfrac{1}{l}$
B. $\Delta l$ versus $l^2$ ✓ Correct
C. $\Delta l$ versus $\dfrac{1}{l^2}$
D. $\Delta l$ versus $l$
Solution: $Y=\dfrac{Fl}{A\Delta l}$ and $V=Al$ is constant $\Rightarrow \Delta l=\dfrac{F}{VY}l^2$, so $\Delta l\propto l^2$ (a straight line vs $l^2$).
Q5 — Stress, Strain and Hooke's Laws · medium · numerical
The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?
A. Length $=50$ cm, diameter $=0.5$ mm ✓ Correct
B. Length $=100$ cm, diameter $=1$ mm
C. Length $=200$ cm, diameter $=2$ mm
D. Length $=300$ cm, diameter $=3$ mm
Solution: $\Delta L=\dfrac{FL}{YA}\propto\dfrac{L}{d^2}$. Values of $L/d^2$: (a) $50/0.25=200$, (b) $100/1=100$, (c) $200/4=50$, (d) $300/9\approx33$. Largest for option (a).
Q6 — Stress-Strain Curve, Thermal Stress and Elastic PE · medium · theory
The stress-strain curves are drawn for two different materials $X$ and $Y$. It is observed that the ultimate strength point and the fracture point are close to each other for material $X$ but are far apart for material $Y$. We can say that materials $X$ and $Y$ are likely to be (respectively)
A. ductile and brittle
B. brittle and ductile ✓ Correct
C. brittle and plastic
D. plastic and ductile
Solution: If the ultimate strength point and fracture point are close, the material breaks soon after its strength limit — it is brittle ($X$). If they are far apart, the material withstands large strain before fracturing — it is ductile ($Y$).
Q7 — Stress-Strain Curve, Thermal Stress and Elastic PE · medium · numerical
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
A. $MgL$
B. $\dfrac{1}{2}Mgl$ ✓ Correct
C. $\dfrac{1}{2}MgL$
D. $Mgl$
Solution: Elastic PE $=\dfrac{1}{2}\times$ force $\times$ elongation $=\dfrac{1}{2}\times Mg\times l=\dfrac{1}{2}Mgl$.