Tag: properties of material substances

Questions Related to properties of material substances

In an experiment on the determination of Young's Modulus of a wire by Searle's method, following data is available:
Normal length of the wire (L) = $110$cm
Diameter of the wire (d) = $0.01cm$
Elongation in the wire(l) = $0.125cm$
This elongation is for a tension of $50$N. The least counts for corresponding quantities are $0.01cm, 0.00005 cm, $ and $0.001cm$, respectively. Calculate the maximum error in calculating the value of Young's modulus(Y).

elastic energy properties of material substances elasticity properties of matter physics

  1. $8\%$

  2. $1.809\%$

  3. $1.09\%$

  4. cant say

Show answer
Correct Option: B

When a weight of 5 kg is suspended from a copper wire of length 30 m and diameter 0.5 mm, the length of the wire increases by 2.4 cm. If the diameter is doubled, the extension produced is :

elastic energy properties of material substances elasticity properties of matter physics

  1. 1.2 cm

  2. 0.6

  3. 0.3 cm

  4. 0.15 cm

Show answer
Correct Option: B
Explanation:

$Y \, = \, \dfrac{Mg \, \times \, 4 \, \times \, 1}{\pi D^2 \, \times \, \Delta l} \, or \, \Delta l \, \propto \, \dfrac{1}{D^2}$
(i) when D is double, $\Delta l$ becomes one-fourth. i.e.,
$\dfrac{1}{4} \, \times \, 2.4 \, cm \, i.e., 0.6 \, cm \, \times \, 2.4 \, cm$ i.e. 0.6 cm.

The maximum load a wire can with stand without breaking, when it is stretched to twice of its original length, will:

elastic energy properties of material substances elasticity properties of matter physics

  1. be half

  2. be four time decreased

  3. be double

  4. remain same

Show answer
Correct Option: D
Explanation:

the maximum load a wire can with stand without breaking it is stretched to twice of its original length is remain same$.$

Hence,
option $(D)$ is correct answer.

A uniform wire of length L and radius r is twisted by a angle $ \angle \alpha$. If modulus of rigidity of the wire is $ \eta  $, then the elastic potential energy stored in wire, is

elastic energy properties of material substances elasticity properties of matter physics

  1. $ \frac{\pi \eta r^{4}\alpha }{2L^{2}} $

  2. $ \frac{\pi \eta r^{4}\alpha^{2} }{4L} $

  3. $ \frac{\pi \eta r^{4}\alpha }{4L^{2}} $

  4. $ \frac{\pi \eta r^{4}\alpha^{2} }{2L} $

Show answer
Correct Option: B

The length of an elastic string is $x$ metre when the tension is $8\ N$. Its length is $y$ metre when the tension is $10\ N$. What will be its length, when the tension is $18\ N$?

elastic energy properties of material substances elasticity properties of matter physics

  1. $2x + y$

  2. $5y - 4x$

  3. $7y - 5x$

  4. $7y + 5x$

Show answer
Correct Option: B
Explanation:

Let, original length of the spring is L metre and, Y = $\dfrac { F.L }{ A.l } $

Now, when F = 8N, and l = (x - l)m then, $Y=\dfrac { 8.L }{ A.\left( x-L \right)  } \quad \longrightarrow (I)$
and when F=10N, and l = (y - l)m then, $y=\dfrac { 10.L }{ A.\left( y-L \right)  } m\quad \longrightarrow (II)$
From equation (I) and (II) we get,
$\dfrac { 8L }{ A\left( x-L \right)  } =\dfrac { 10L }{ A\left( y-L \right)  } $
or,  $8\left( y-L \right) =10\left( x-L \right) $
or,    $4y-4L=5x-5L$
or,                $L=5x-4y$
When, F=18N,
Let, length of the wire will be Z metre.
$\therefore \quad Y=\dfrac { 18.L }{ A.\left( Z-L \right)  } \quad \longrightarrow (III)$
From equation (I) and (III) we get,
$\dfrac { 8L }{ A\left( x-L \right)  } =\dfrac { 18L }{ A\left( Z-L \right)  } $
or,  $9\left( x-L \right) =4\left( Z-L \right) $
or,  $4Z=9x-9L+4L$
            $=9x-5L$
            $=9x-25x+20y$    [putting value of L]
or,  $Z=5y-4x$


Work done by restoring force in a string within elastic limit is $-10\ J$. The maximum amount of heat produced in the string is :

elastic energy properties of material substances elasticity properties of matter physics

  1. $10\ J$

  2. $20\ J$

  3. $5\ J$

  4. $15\ J$

Show answer
Correct Option: A

If work done in stretching a wire by 1 mm is 2J. Then the work necessary for stretching another wire of same material but with double the radius and half the length by 1 mm in joule is

elastic energy properties of material substances elasticity properties of matter physics

  1. 1/4

  2. 4

  3. 8

  4. 16

Show answer
Correct Option: D
Explanation:

The stretching force $F=\dfrac{YA\Delta l}{l}$

where $Y=$Young's modulus, $A=$Area of cross-section of wire, $l=$actual length of wire, $\Delta l=$increase in length.
$F=\dfrac{Y\pi r^{2}\Delta l}{l}$
As the material is same $Y$ does not change.
$\dfrac{F _1}{F _2}=\dfrac{\dfrac{r _1^{2}\Delta l _1}{l _1}}{\dfrac{r _2^{2}\Delta l _2}{l _2}}$
Here $\Delta l _1=1mm$
$\Delta l _2=1mm$
$l _2=\dfrac{1}{2}l _1$
$r _2=2r _1$
$\dfrac{F _1}{F _2}=\dfrac{\dfrac{r _1^{2}\times 1mm}{l _1}}{\dfrac{4r _1^{2}\times 1mm}{\dfrac{1}{2}l _1}}$
$\dfrac{F _1}{F _2}=\dfrac{1}{8}$
The work done in stretching wire by amount $\Delta l$ is $W=\dfrac{1}{2} F\Delta l$
Hence $\dfrac{W _1}{W _2}=\dfrac{F _1}{F _2}=\dfrac{1}{8}$
As $F _1=2$
$F _2=2\times 8=16$
Hence the correct option is (D).

When a body mass $M$ is attached to power end of a wire (of length $L$) whose upper end is fixed, then the elongation of the wire is $l$. In this situation mark out the correct statement(s).

elastic energy properties of material substances elasticity properties of matter physics

  1. Loss in gravitational potential energy of $M$ is $Mgl$.

  2. Elastic potential energy stored in the wire is $\dfrac {Mgl}{2}$

  3. Elastic potential energy stored in the wire is $Mgl$

  4. Elastic potential energy stored in the wire is $\dfrac {Mgl}{3}$

Show answer
Correct Option: A,B
Explanation:

Since it moves $l$ distance against gravity, so gravitational potential energy=Mgl
Elastic potential energy=$1/2\times Stress\times Strain\times Volume=1/2\times \dfrac{Mg}{A} \times \dfrac{l}{L}\times AL=\dfrac{Mgl}{2}$

A material has Poisson's ratio $0.5$. if a uniform rod of it suffers a longitudinal strain of $2\times {10}^{3}$, then the percentage change in volume is

physics properties of material substances poisson ratio poisson's ratio elastic energy

  1. $0.6$

  2. $0.4$

  3. $0.2$

  4. zero

Show answer
Correct Option: D
Explanation:

Poisson's ratio is a material property. Therefore it doesn't change with dimensions.  

Option D

Which of the following statements is correct regarding Poisson's ratio?

physics properties of material substances poisson ratio poisson's ratio elastic energy

  1. It is the ratio of the longitudinal strain to the lateral strain

  2. Its value is independent of the nature of the material

  3. It is unitless and dimensionless quantity

  4. The practical value of Poisson's ratio lies between $0$ and $1$

Show answer
Correct Option: C
Explanation:

The ratio of the lateral strain to longitudinal strain is called Poisson's ratio.
Hence, option (a) is an incorrect statement.
Its value depends only on the nature of the material. 
Hence, option (b) is an incorrect statement.
It is the ratio of two like physical quantities.
Therefore, it is unitless and dimensionless quantity.
Hence option (c) is a correct statement
The practical value of Poisson's ratio lies between $0$ and $0.5$
hence option (d) is an incorrect statement.