Properties of Solids and Liquids — DPP 1

20 NEET questions from Properties of Solids and Liquids, with answers and explanations. Attempt it as a timed test to get scoring, accuracy breakdown and mistake tracking.

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1
For a constant hydraulic stress on an object, the fractional change in the object's volume $\left( \frac { \Delta V } { V } \right)$ and its bulk modulus (B) are related as :
  1. A $\frac { \Delta V } { V } \propto B$
  2. B $\frac { \Delta V } { V } \propto \frac { 1 } { B }$
  3. C $\frac { \Delta V } { V } \propto B ^ { 2 }$
  4. D $\frac { \Delta V } { V } \propto B ^ { - 2 }$
Show answer & explanation

Correct answer: B

For volume
Stress = ∆P
Properties of Solids and Liquids – NEET-7636
2
The Young's modulus of a rubber string 8 cm long and density $1.5 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ is $5 \times 10 ^ { 8 } \mathrm {~N} / \mathrm { m } ^ { 2 }$, is suspended on the ceiling in a room. The increase in length due to its own weight will be :
  1. A $9.6 \times 10 ^ { - 5 } \mathrm {~m}$
  2. B $9.6 \times 10 ^ { - 11 } \mathrm {~m}$
  3. C $9.6 \times 10 ^ { - 3 } \mathrm {~m}$
  4. D 9.6 m
Show answer & explanation

Correct answer: B

$\begin{aligned} \Delta \mathrm{L}=\frac{\rho \mathrm{gL}^{2}}{2 \mathrm{Y}}= & \frac{1.5 \times 10 \times 64 \times 10^{-4}}{2 \times 5 \times 10^{8}} \\ & =9.6 \times 10^{-11} \mathrm{~m}\end{aligned}$
3
The diameter of a brass rod is 4 mm and Young's modulus of brass is $9 \times 10 ^ { 10 } \mathrm {~N} / \mathrm { m } ^ { 2 }$. The force required to stretch by 0.1% of its length is :
  1. A $360 \pi \mathrm {~N}$
  2. B 36 N
  3. C $144 \pi \times 10 ^ { 3 } \mathrm {~N}$
  4. D $36 \pi \times 10 ^ { 5 } \mathrm {~N}$
Show answer & explanation

Correct answer: A

Properties of Solids and Liquids – NEET-7631
4
The load versus elongation graph for four wires of the same material and same length is shown in the figure. The thinnest wire is represented by the line.
Properties of Solids and Liquids – NEET-7629
  1. A OA
  2. B OB
  3. C OC
  4. D OD
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Correct answer: A

Properties of Solids and Liquids – NEET-7629
5
When a tension F is applied in uniform wire of length l and radius r, the elongation produced is e. When tension 2F is applied, the elongation produced in another uniform wire of length 2l and radius 2r made of same material is :-
  1. A 0.5 e
  2. B 1.0 e
  3. C 1.5 e
  4. D 2.0 e
Show answer & explanation

Correct answer: B

Properties of Solids and Liquids – NEET-7627
6
A wire elongates by l mm when a load W is hanged from it. If the wire goes over a pulley and two weights W each are hung at the two ends, the elongation of the wire will be (in mm)-
  1. A $\ell$
  2. B $2 \ell$
  3. C zero
  4. D $\ell / 2$
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Correct answer: A

In both case tension in wire are same and Δl ∝ T
7
One end of uniform wire of length L and of weight W is attached rigidly to a point in the roof and a weight W$_{1}$ is suspended from its lower end. If s is the area of cross-section of the wire, the stress in the wire at a height (L/4) from its lower end is
  1. A $\frac { W _ { 1 } } { s }$
  2. B $\frac { \left[ W _ { 1 } + \frac { W } { 4 } \right] } { s }$
  3. C $\frac { \left[ \mathrm { W } _ { 1 } + \frac { 3 \mathrm {~W} } { 4 } \right] } { \mathrm { s } }$
  4. D $\frac { W _ { 1 } + W } { 4 }$
Show answer & explanation

Correct answer: B

Properties of Solids and Liquids – NEET-7603
8
How much force is required to produce an increase of 0.2% in the length of a brass wire of diameter 0.6 mm? [Young's modulus for brass $= 0.9 \times 10 ^ { 11 } \mathrm {~N} / \mathrm { m } ^ { 2 }$ ]
  1. A Nearly 17 N
  2. B Nearly 34 N
  3. C Nearly 51 N
  4. D Nearly 68 N
Show answer & explanation

Correct answer: C

$\begin{array}{l}\mathrm{F}=\frac{\mathrm{YA}}{\mathrm{L}} \Delta \ell \\ =0.9 \times 10^{11} \times \pi \times\left(0.3 \times 10^{-3}\right)^{2} \times \frac{0.2}{100}=51 \mathrm{~N}\end{array}$
9
The dimensions of two wires A and B are the same. But their materials are different. Their load-extension graphs are shown. If Y$_{A}$ and Y$_{B}$ are the values of Young's modulus of elasticity of A and B, respectively, then
Properties of Solids and Liquids – NEET-7605
  1. A $Y _ { A } > Y _ { B }$
  2. B $Y _ { A } < Y _ { B }$
  3. C $Y _ { A } = Y _ { B }$
  4. D $\mathrm { Y } _ { \mathrm { B } } = 2 \mathrm { Y } _ { \mathrm { A } }$
Show answer & explanation

Correct answer: A

From graph
$\begin{array}{l}\text { Slope }=\frac{\mathrm{F}}{\Delta \ell} \\ \text { also } \mathrm{Y}=\frac{\mathrm{FL}}{\mathrm{A} \Delta \ell} \\ \text { Slope }=\frac{\mathrm{F}}{\Delta \ell}=\mathrm{Y} \frac{\mathrm{A}}{\mathrm{L}}\end{array}$
⇒ more slope, more Y
So $Y_{A}>Y_{B}$
10
If the strain in a wire is not more than $\frac{1}{1000}$ and Y = 2 × 10$^{11}$ N/m$^{2}$, Diameter of wire is 1 mm. The maximum weight hung from the wire is:-
  1. A 110 N
  2. B 125 N
  3. C 157 N
  4. D 168 N
Show answer & explanation

Correct answer: C

$\begin{aligned} \mathrm{F} & =\frac{\mathrm{YA}}{\mathrm{L}} \Delta \ell=\pi \times\left(\frac{1}{2} \times 10^{-3}\right)^{2} \times 2 \times 10^{11} \times \frac{1}{1000} \\ & =157 \mathrm{~N}\end{aligned}$
11
Two wires of the same material and length but with diameters in the ratio 1 : 2 are stretched by the same force. The potential energy per unit volume for the two wires when stretched will be in the ratio.
  1. A 16 : 1
  2. B 4 : 1
  3. C 2 : 1
  4. D 1 : 1
Show answer & explanation

Correct answer: A

Potential energy per unit volume is
$=\frac{1}{2} \times \frac{(\text { Stress })^{2}}{\mathrm{Y}} \Rightarrow \frac{\mathrm{U}_{1}}{\mathrm{U}_{2}}=\frac{\mathrm{F}_{1}^{2}}{\mathrm{~A}_{1}^{2}} \times \frac{\mathrm{A}_{2}^{2}}{\mathrm{~F}_{2}^{2}}=\frac{\mathrm{r}_{2}^{4}}{\mathrm{r}_{1}^{4}}=16: 1$
12
For steel, the breaking stress is $6 \times 10 ^ { 6 } \mathrm {~N} / \mathrm { m } ^ { 2 }$ and the density is $8 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$. The maximum length of steel wire, which can be suspended without breaking under its own weight, is [g = 10 m/s$^{2}$]
  1. A 140 m
  2. B 120 m
  3. C 75 m
  4. D 200 m
Show answer & explanation

Correct answer: C

Properties of Solids and Liquids – NEET-7604
13
Two wires of the same length and material but different radii r$_{1}$ and r$_{2}$ are suspended from a rigid support both carry the same load at the lower end. The ratio of the stress developed in the second wire to that developed in the first wire is -
  1. A $\frac { r _ { 1 } } { r _ { 2 } }$
  2. B $\frac { r _ { 1 } ^ { 2 } } { r _ { 2 } ^ { 2 } }$
  3. C $\left( \frac { r _ { 1 } } { r _ { 2 } } \right) ^ { 5 / 2 }$
  4. D $\left( \frac { r _ { 1 } } { r _ { 2 } } \right) ^ { 1 / 2 }$
Show answer & explanation

Correct answer: B

Properties of Solids and Liquids – NEET-7633
14
A wire of length L and cross-sectional area A is made of a material of Young's modulus Y. The work done in stretching the wire by an amount x is given by :-
  1. A $\frac { Y A x ^ { 2 } } { L }$
  2. B $\frac { \mathrm { YAx } ^ { 2 } } { 2 \mathrm {~L} }$
  3. C $\frac { Y A L ^ { 2 } } { x }$
  4. D $\frac { \mathrm { YAL } ^ { 2 } } { 2 \mathrm { x } }$
Show answer & explanation

Correct answer: B

For a wire of length L stretched by a length x, the restoring elastic force is :
$F=\left[\frac{x}{L}\right] Y A$
The work required to be done against the elastic restoring forces to elongate it further by a length dx is,
$\mathrm{dW}=\mathrm{F} \cdot \mathrm{dx}=\frac{\mathrm{YA}}{\mathrm{L}} \mathrm{x} \cdot \mathrm{dx}$
The total work done in stretching the wire from x = 0 to x is,
$W=\int_{0}^{x} \frac{Y A}{L} x \cdot d x=\frac{Y A}{L}\left[\frac{x^{2}}{2}\right]$
15
If 'S' is stress and 'Y' is Young's modulus of material of a wire, the energy stored in the wire per unit volume is
  1. A $\frac { S } { 2 Y }$
  2. B $\frac { 2 Y } { S ^ { 2 } }$
  3. C $\frac { S ^ { 2 } } { 2 Y }$
  4. D $2 \mathrm {~S} ^ { 2 } \mathrm { Y }$
Show answer & explanation

Correct answer: C

Energy density $=\frac{1}{2} \times \frac{(\text { Stress })^{2}}{\mathrm{Y}}=\frac{\mathrm{S}^{2}}{2 \mathrm{Y}}$
16
Poisson's ratio can not have the value :
  1. A 0.1
  2. B 0.7
  3. C 0.2
  4. D 0.5
Show answer

Correct answer: B

17
The lower surface of a cube is fixed. On its upper surface, force is applied at an angle of $30 ^ { \circ }$ from its surface. The change will be in its
  1. A shape
  2. B size
  3. C volume
  4. D both shape and size
Show answer

Correct answer: D

18
A ball falling in a lake of depth 200 m shows 0.1% decrease in its volume at the bottom. What is the bulk modulus of the material of the ball?
  1. A $19.6 \times 10 ^ { 8 } \mathrm {~N} / \mathrm { m } ^ { 2 }$
  2. B $19.6 \times 10 ^ { - 10 } \mathrm {~N} / \mathrm { m } ^ { 2 }$
  3. C $19.6 \times 10 ^ { 10 } \mathrm {~N} / \mathrm { m } ^ { 2 }$
  4. D $19.6 \times 10 ^ { - 8 } \mathrm {~N} / \mathrm { m } ^ { 2 }$
Show answer & explanation

Correct answer: A

$\begin{array}{l}\text { Bulk modulus }=\frac{\Delta \mathrm{P}}{\Delta \mathrm{V} / \mathrm{V}}=\frac{\mathrm{h} \rho \mathrm{g}}{0.1 / 100} \\ =\frac{200 \times 10^{3} \times 9.8 \times 100}{0.1}=19.6 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}\end{array}$
19
A fixed volume of iron is drawn into a wire of length $\ell$. The extension produced in this wire by a constant force F is proportional to -
  1. A $\frac { 1 } { \ell ^ { 2 } }$
  2. B $\frac { 1 } { \ell }$
  3. C $\ell ^ { 2 }$
  4. D $\ell$
Show answer & explanation

Correct answer: C

Volume = constant
$\begin{array}{l}\mathrm{A} \times \ell=\mathrm{constant} \Rightarrow \mathrm{A} \propto \frac{1}{\ell} \\ \Delta \ell=\frac{\mathrm{F} \ell}{\mathrm{AY}} \Rightarrow \Delta \ell \propto \frac{\ell}{\mathrm{A}} \Rightarrow \Delta \ell \propto \ell^{2} \quad\left(\text { as } \mathrm{A} \propto \frac{1}{\ell}\right)\end{array}$
20
A mass of 0.5 kg is suspended from wire, then length of wire increase by 3 mm then find out work done :
  1. A $4.5 \times 10 ^ { - 3 } \mathrm {~J}$
  2. B $7.3 \times 10 ^ { - 3 } \mathrm {~J}$
  3. C $9.3 \times 10 ^ { - 2 } \mathrm {~J}$
  4. D $2.5 \times 10 ^ { - 2 } \mathrm {~J}$
Show answer & explanation

Correct answer: B

Properties of Solids and Liquids – NEET-7625

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