Physics
General
Easy

Question

The ratio of pathlength and the respective time interval is

  1. Mean velocity
  2. Mean speed
  3. instantaneous velocity
  4. instantaneous speed

The correct answer is: Mean speed

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Related Questions to study

General
physics

A particle is thrown in upward direction with initial velocity of 60 m/s. Find average speed and average velocity after 10 seconds. [g =10 MS2]

A particle is thrown in upward direction with initial velocity of 60 m/s. Find average speed and average velocity after 10 seconds. [g =10 MS2]

physicsGeneral
General
physics-

The work done in deforming body is given by

Let L be length of body, A the area of cross-section and l the increase in length.
S t r e s s equals fraction numerator F over denominator A to the power of ´ end exponent end fraction s t r a i n equals fraction numerator l over denominator L end fraction
Force necessary to deform the body is
F equals fraction numerator Y A over denominator L end fraction l
If body is deformed by a distance, then
W o r k blank d o n e equals F cross times d l equals fraction numerator Y A over denominator L end fraction l d l
W equals not stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator Y A over denominator L end fraction l d l equals fraction numerator Y A over denominator L end fraction open square brackets fraction numerator l to the power of 2 end exponent over denominator 2 end fraction close square brackets subscript 0 end subscript superscript l end superscript equals fraction numerator 1 over denominator 2 end fraction Y A fraction numerator l to the power of 2 end exponent over denominator L end fraction
equals fraction numerator 1 over denominator 2 end fraction open parentheses Y fraction numerator l over denominator L end fraction close parentheses open parentheses fraction numerator l over denominator L end fraction close parentheses open parentheses A L close parentheses
equals fraction numerator 1 over denominator 2 end fraction open parentheses s t r e s s cross times s t r a i n close parentheses cross times v o l u m e
Hence, work done for unit volume is
W equals fraction numerator 1 over denominator 2 end fraction s t r e s s cross times s r a i n.

The work done in deforming body is given by

physics-General
Let L be length of body, A the area of cross-section and l the increase in length.
S t r e s s equals fraction numerator F over denominator A to the power of ´ end exponent end fraction s t r a i n equals fraction numerator l over denominator L end fraction
Force necessary to deform the body is
F equals fraction numerator Y A over denominator L end fraction l
If body is deformed by a distance, then
W o r k blank d o n e equals F cross times d l equals fraction numerator Y A over denominator L end fraction l d l
W equals not stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator Y A over denominator L end fraction l d l equals fraction numerator Y A over denominator L end fraction open square brackets fraction numerator l to the power of 2 end exponent over denominator 2 end fraction close square brackets subscript 0 end subscript superscript l end superscript equals fraction numerator 1 over denominator 2 end fraction Y A fraction numerator l to the power of 2 end exponent over denominator L end fraction
equals fraction numerator 1 over denominator 2 end fraction open parentheses Y fraction numerator l over denominator L end fraction close parentheses open parentheses fraction numerator l over denominator L end fraction close parentheses open parentheses A L close parentheses
equals fraction numerator 1 over denominator 2 end fraction open parentheses s t r e s s cross times s t r a i n close parentheses cross times v o l u m e
Hence, work done for unit volume is
W equals fraction numerator 1 over denominator 2 end fraction s t r e s s cross times s r a i n.
General
physics-

A wire of length 2 L and radius r is stretched between A and B without the application of any tension. If Y is the Young’s modulus of the wire and it is stretched like A C B, then the tension in the wire will be

T equals fraction numerator Y A l over denominator L end fraction
Increase in length of one segment of wire
l equals open parentheses L plus fraction numerator 1 over denominator 2 end fraction fraction numerator d to the power of 2 end exponent over denominator L end fraction close parentheses minus L equals fraction numerator 1 over denominator 2 end fraction fraction numerator d to the power of 2 end exponent over denominator L end fraction
So, T equals fraction numerator Y pi r to the power of 2 end exponent. d to the power of 2 end exponent over denominator 2 L to the power of 2 end exponent end fraction

A wire of length 2 L and radius r is stretched between A and B without the application of any tension. If Y is the Young’s modulus of the wire and it is stretched like A C B, then the tension in the wire will be

physics-General
T equals fraction numerator Y A l over denominator L end fraction
Increase in length of one segment of wire
l equals open parentheses L plus fraction numerator 1 over denominator 2 end fraction fraction numerator d to the power of 2 end exponent over denominator L end fraction close parentheses minus L equals fraction numerator 1 over denominator 2 end fraction fraction numerator d to the power of 2 end exponent over denominator L end fraction
So, T equals fraction numerator Y pi r to the power of 2 end exponent. d to the power of 2 end exponent over denominator 2 L to the power of 2 end exponent end fraction
General
physics-

A cube of aluminium of sides 0.1 m is subjected to a sharing force of 100 N. The top face of the cube is displaced through 0.02 cm with respect to the bottom face. The shearing strain would be

Shearing strain = fraction numerator 0.02 blank cross times 10 to the power of negative 2 end exponent over denominator 0.1 blank end fraction equals 0.002

A cube of aluminium of sides 0.1 m is subjected to a sharing force of 100 N. The top face of the cube is displaced through 0.02 cm with respect to the bottom face. The shearing strain would be

physics-General
Shearing strain = fraction numerator 0.02 blank cross times 10 to the power of negative 2 end exponent over denominator 0.1 blank end fraction equals 0.002
General
physics-

A uniform slender rod of length L, cross-sectional area A and Young’s modulus Y is acted upon by the forces shown in the figure. The elongation of the rod is

Net elongation of the rod is

l equals blank fraction numerator 3 F open parentheses fraction numerator 2 L over denominator 3 end fraction close parentheses over denominator A Y end fraction plus fraction numerator 2 F open parentheses fraction numerator L over denominator 3 end fraction close parentheses over denominator A Y end fraction
l equals fraction numerator 8 F L over denominator 3 A Y end fraction

A uniform slender rod of length L, cross-sectional area A and Young’s modulus Y is acted upon by the forces shown in the figure. The elongation of the rod is

physics-General
Net elongation of the rod is

l equals blank fraction numerator 3 F open parentheses fraction numerator 2 L over denominator 3 end fraction close parentheses over denominator A Y end fraction plus fraction numerator 2 F open parentheses fraction numerator L over denominator 3 end fraction close parentheses over denominator A Y end fraction
l equals fraction numerator 8 F L over denominator 3 A Y end fraction
General
physics-

The graph shows the behaviour of a length of wire in the region for which the substance obeys Hooke’s law. P and Q represent

Graph between applied force and extension will be straight line because in elastic range
Applied force proportional to extension
But the graph between extension and stored elastic energy will be parabolic in nature
As U equals 1 divided by 2 blank k x to the power of 2 end exponent or U proportional to x to the power of 2 end exponent

The graph shows the behaviour of a length of wire in the region for which the substance obeys Hooke’s law. P and Q represent

physics-General
Graph between applied force and extension will be straight line because in elastic range
Applied force proportional to extension
But the graph between extension and stored elastic energy will be parabolic in nature
As U equals 1 divided by 2 blank k x to the power of 2 end exponent or U proportional to x to the power of 2 end exponent
General
physics-

If the shear modulus of a wire material is 5.9blank cross times 10 to the power of 11 end exponent d y n e blank c m to the power of negative 2 end exponent then the potential energy of a wire of 4 cross times 10 to the power of 3 end exponent c m in diameter and 5 cm long twisted through an angle of 10’ , is

To twist the wire through the angle d theta comma blankit is necessary to do the work
d W equals blank tau d theta
And theta equals 10 to the power of ´ end exponent equals fraction numerator 10 over denominator 60 end fraction cross times fraction numerator pi over denominator 180 end fraction equals fraction numerator pi over denominator 1080 end fraction r a d
W equals blank not stretchy integral from 0 to theta of tau blank d theta equals blank not stretchy integral from 0 to theta of fraction numerator eta pi r to the power of 4 end exponent theta d theta over denominator 2 l end fraction equals blank fraction numerator eta pi r to the power of 4 end exponent theta over denominator 4 l end fraction
W equals blank fraction numerator 5.9 blank cross times 10 to the power of 11 end exponent cross times 10 to the power of negative 5 end exponent cross times blank pi open parentheses 2 cross times 10 to the power of negative 5 end exponent close parentheses to the power of 4 end exponent pi to the power of 2 end exponent over denominator 10 to the power of negative 4 end exponent cross times 4 cross times 5 cross times 10 to the power of negative 2 end exponent cross times open parentheses 1080 close parentheses to the power of 2 end exponent end fraction
W equals 1.253 blank cross times 10 to the power of negative 12 end exponent blank J

If the shear modulus of a wire material is 5.9blank cross times 10 to the power of 11 end exponent d y n e blank c m to the power of negative 2 end exponent then the potential energy of a wire of 4 cross times 10 to the power of 3 end exponent c m in diameter and 5 cm long twisted through an angle of 10’ , is

physics-General
To twist the wire through the angle d theta comma blankit is necessary to do the work
d W equals blank tau d theta
And theta equals 10 to the power of ´ end exponent equals fraction numerator 10 over denominator 60 end fraction cross times fraction numerator pi over denominator 180 end fraction equals fraction numerator pi over denominator 1080 end fraction r a d
W equals blank not stretchy integral from 0 to theta of tau blank d theta equals blank not stretchy integral from 0 to theta of fraction numerator eta pi r to the power of 4 end exponent theta d theta over denominator 2 l end fraction equals blank fraction numerator eta pi r to the power of 4 end exponent theta over denominator 4 l end fraction
W equals blank fraction numerator 5.9 blank cross times 10 to the power of 11 end exponent cross times 10 to the power of negative 5 end exponent cross times blank pi open parentheses 2 cross times 10 to the power of negative 5 end exponent close parentheses to the power of 4 end exponent pi to the power of 2 end exponent over denominator 10 to the power of negative 4 end exponent cross times 4 cross times 5 cross times 10 to the power of negative 2 end exponent cross times open parentheses 1080 close parentheses to the power of 2 end exponent end fraction
W equals 1.253 blank cross times 10 to the power of negative 12 end exponent blank J
General
physics-

The Young’s modulus of the material of a wire is equal to the

Young’s modulus of material Y equals fraction numerator L i n e a r blank s t r e s s over denominator L o n g i t u d i n a l blank s t r a i n end fraction
If longitudinal strain is equal unity, then
Y equals Linear stress produced

The Young’s modulus of the material of a wire is equal to the

physics-General
Young’s modulus of material Y equals fraction numerator L i n e a r blank s t r e s s over denominator L o n g i t u d i n a l blank s t r a i n end fraction
If longitudinal strain is equal unity, then
Y equals Linear stress produced
General
Maths-

y equals f left parenthesis x right parenthesis equals fraction numerator x over denominator 1 plus vertical line x vertical line end fraction comma x element of R comma y element of R text  is  end text

w e space h a v e comma space
f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator x over denominator 1 plus x end fraction comma space i f space x greater or equal than 0 end cell row cell fraction numerator x over denominator 1 minus x end fraction comma space i f space x less or equal than 0 end cell end table close
C a s e space i comma space w h e n space x greater or equal than 0
f left parenthesis x right parenthesis equals fraction numerator x over denominator 1 plus x end fraction
t h e n comma space f left parenthesis x subscript 1 right parenthesis equals f left parenthesis x subscript 2 right parenthesis rightwards double arrow fraction numerator x subscript 1 over denominator 1 plus x subscript 1 end fraction equals fraction numerator x subscript 2 over denominator 1 plus x subscript 2 end fraction rightwards double arrow x subscript 1 plus x subscript 1 x subscript 2 equals x subscript 2 plus x subscript 1 x subscript 2 rightwards double arrow x subscript 1 equals x subscript 2
S o comma space f space i s space o n e minus space o n e.
L e t space y element of R
a n d space y equals fraction numerator x over denominator 1 plus x end fraction rightwards double arrow y plus x y equals x rightwards double arrow x left parenthesis 1 minus y right parenthesis equals y rightwards double arrow x equals fraction numerator y over denominator 1 minus y end fraction
N o w comma space f open parentheses fraction numerator y over denominator 1 minus y end fraction close parentheses equals fraction numerator fraction numerator y over denominator 1 minus y end fraction over denominator 1 plus fraction numerator y over denominator 1 minus y end fraction end fraction equals fraction numerator y over denominator 1 minus y plus y end fraction equals y
S o comma space f left parenthesis x right parenthesis space i s space o n t o.

C a s e space i comma space w h e n space x less or equal than 0
f left parenthesis x right parenthesis equals fraction numerator x over denominator 1 minus x end fraction
t h e n comma space f left parenthesis x subscript 1 right parenthesis equals f left parenthesis x subscript 2 right parenthesis rightwards double arrow fraction numerator x subscript 1 over denominator 1 minus x subscript 1 end fraction equals fraction numerator x subscript 2 over denominator 1 minus x subscript 2 end fraction rightwards double arrow x subscript 1 minus x subscript 1 x subscript 2 equals x subscript 2 minus x subscript 1 x subscript 2 rightwards double arrow x subscript 1 equals x subscript 2
S o comma space f space i s space o n e minus space o n e.
L e t space y element of R
a n d space y equals fraction numerator x over denominator 1 minus x end fraction rightwards double arrow y minus x y equals x rightwards double arrow x left parenthesis 1 plus y right parenthesis equals y rightwards double arrow x equals fraction numerator y over denominator 1 plus y end fraction
N o w comma space f open parentheses fraction numerator y over denominator 1 plus y end fraction close parentheses equals fraction numerator fraction numerator y over denominator 1 plus y end fraction over denominator 1 minus fraction numerator y over denominator 1 plus y end fraction end fraction equals fraction numerator y over denominator 1 plus y minus y end fraction equals y
S o comma space f left parenthesis x right parenthesis space i s space o n t o.

y equals f left parenthesis x right parenthesis equals fraction numerator x over denominator 1 plus vertical line x vertical line end fraction comma x element of R comma y element of R text  is  end text

Maths-General
w e space h a v e comma space
f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator x over denominator 1 plus x end fraction comma space i f space x greater or equal than 0 end cell row cell fraction numerator x over denominator 1 minus x end fraction comma space i f space x less or equal than 0 end cell end table close
C a s e space i comma space w h e n space x greater or equal than 0
f left parenthesis x right parenthesis equals fraction numerator x over denominator 1 plus x end fraction
t h e n comma space f left parenthesis x subscript 1 right parenthesis equals f left parenthesis x subscript 2 right parenthesis rightwards double arrow fraction numerator x subscript 1 over denominator 1 plus x subscript 1 end fraction equals fraction numerator x subscript 2 over denominator 1 plus x subscript 2 end fraction rightwards double arrow x subscript 1 plus x subscript 1 x subscript 2 equals x subscript 2 plus x subscript 1 x subscript 2 rightwards double arrow x subscript 1 equals x subscript 2
S o comma space f space i s space o n e minus space o n e.
L e t space y element of R
a n d space y equals fraction numerator x over denominator 1 plus x end fraction rightwards double arrow y plus x y equals x rightwards double arrow x left parenthesis 1 minus y right parenthesis equals y rightwards double arrow x equals fraction numerator y over denominator 1 minus y end fraction
N o w comma space f open parentheses fraction numerator y over denominator 1 minus y end fraction close parentheses equals fraction numerator fraction numerator y over denominator 1 minus y end fraction over denominator 1 plus fraction numerator y over denominator 1 minus y end fraction end fraction equals fraction numerator y over denominator 1 minus y plus y end fraction equals y
S o comma space f left parenthesis x right parenthesis space i s space o n t o.

C a s e space i comma space w h e n space x less or equal than 0
f left parenthesis x right parenthesis equals fraction numerator x over denominator 1 minus x end fraction
t h e n comma space f left parenthesis x subscript 1 right parenthesis equals f left parenthesis x subscript 2 right parenthesis rightwards double arrow fraction numerator x subscript 1 over denominator 1 minus x subscript 1 end fraction equals fraction numerator x subscript 2 over denominator 1 minus x subscript 2 end fraction rightwards double arrow x subscript 1 minus x subscript 1 x subscript 2 equals x subscript 2 minus x subscript 1 x subscript 2 rightwards double arrow x subscript 1 equals x subscript 2
S o comma space f space i s space o n e minus space o n e.
L e t space y element of R
a n d space y equals fraction numerator x over denominator 1 minus x end fraction rightwards double arrow y minus x y equals x rightwards double arrow x left parenthesis 1 plus y right parenthesis equals y rightwards double arrow x equals fraction numerator y over denominator 1 plus y end fraction
N o w comma space f open parentheses fraction numerator y over denominator 1 plus y end fraction close parentheses equals fraction numerator fraction numerator y over denominator 1 plus y end fraction over denominator 1 minus fraction numerator y over denominator 1 plus y end fraction end fraction equals fraction numerator y over denominator 1 plus y minus y end fraction equals y
S o comma space f left parenthesis x right parenthesis space i s space o n t o.
General
physics-

Two short bar magnets of equal dipole moment M are fastened perpendicularly at their centers, figure. The magnitude of resultant of two magnetic field at a distance d from the center on the bisector of the right angle is

Resolving the magnetic moments along O P and perpendicular toO P comma figure we find that component O P perpendicular O P cancel out. Resultant magnetic moment along O P i s equals M cos invisible function application 45 degree plus M c o s 45 degree

equals 2 blank M c o s blank 45 degree equals fraction numerator 2 M over denominator square root of 2 end fraction equals square root of 2 M
The point P lies on axial line of magnet of moment
equals square root of 2 M
therefore B equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator 2 left parenthesis square root of 2 M right parenthesis over denominator d to the power of 3 end exponent end fraction

Two short bar magnets of equal dipole moment M are fastened perpendicularly at their centers, figure. The magnitude of resultant of two magnetic field at a distance d from the center on the bisector of the right angle is

physics-General
Resolving the magnetic moments along O P and perpendicular toO P comma figure we find that component O P perpendicular O P cancel out. Resultant magnetic moment along O P i s equals M cos invisible function application 45 degree plus M c o s 45 degree

equals 2 blank M c o s blank 45 degree equals fraction numerator 2 M over denominator square root of 2 end fraction equals square root of 2 M
The point P lies on axial line of magnet of moment
equals square root of 2 M
therefore B equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator 2 left parenthesis square root of 2 M right parenthesis over denominator d to the power of 3 end exponent end fraction
General
physics-

Two magnets of equal mass are joined at 90degree each other as shown in figure. Magnet N subscript 1 end subscript S subscript 1 end subscript has a magnetic moment square root of 3 times that of N subscript 2 end subscript S subscript 2 end subscript. The arrangement is pivoted so that it is free to rotate in horizontal plane. When in equilibrium, what angle should N subscript 1 end subscript S subscript 1 end subscript make with magnetic meridian?

In equilibrium, the resultant magnetic moment will be along magnetic meridian. Let N subscript 1 end subscript S subscript 1 end subscript make angle theta with resultant
t a n theta equals fraction numerator M subscript 2 end subscript over denominator M subscript 1 end subscript end fraction equals fraction numerator M over denominator square root of 3 M end fraction equals fraction numerator 1 over denominator square root of 3 end fraction blank therefore theta equals 30 degree

Two magnets of equal mass are joined at 90degree each other as shown in figure. Magnet N subscript 1 end subscript S subscript 1 end subscript has a magnetic moment square root of 3 times that of N subscript 2 end subscript S subscript 2 end subscript. The arrangement is pivoted so that it is free to rotate in horizontal plane. When in equilibrium, what angle should N subscript 1 end subscript S subscript 1 end subscript make with magnetic meridian?

physics-General
In equilibrium, the resultant magnetic moment will be along magnetic meridian. Let N subscript 1 end subscript S subscript 1 end subscript make angle theta with resultant
t a n theta equals fraction numerator M subscript 2 end subscript over denominator M subscript 1 end subscript end fraction equals fraction numerator M over denominator square root of 3 M end fraction equals fraction numerator 1 over denominator square root of 3 end fraction blank therefore theta equals 30 degree
General
physics-

The pressure applied from all directions on a cube is P. How much its temperature should be raised to maintain the original volume? The volume elasticity of the cube is beta and the coefficient of volume expansion is alpha

If coefficient of volume expansion is alpha and rise in temperature is increment theta then increment V equals V alpha increment theta rightwards double arrow fraction numerator increment V over denominator V end fraction equals alpha increment theta
Volume elasticity beta equals fraction numerator P over denominator increment V divided by V end fraction equals fraction numerator P over denominator alpha increment theta end fraction rightwards double arrow increment theta equals fraction numerator P over denominator alpha beta end fraction

The pressure applied from all directions on a cube is P. How much its temperature should be raised to maintain the original volume? The volume elasticity of the cube is beta and the coefficient of volume expansion is alpha

physics-General
If coefficient of volume expansion is alpha and rise in temperature is increment theta then increment V equals V alpha increment theta rightwards double arrow fraction numerator increment V over denominator V end fraction equals alpha increment theta
Volume elasticity beta equals fraction numerator P over denominator increment V divided by V end fraction equals fraction numerator P over denominator alpha increment theta end fraction rightwards double arrow increment theta equals fraction numerator P over denominator alpha beta end fraction
General
physics-

A wire left parenthesis Y equals 2 cross times 10 to the power of 11 end exponent N m to the power of negative 2 end exponent right parenthesis has length 1 m and cross-sectional area 1 m m to the power of negative 2 end exponent. The work required to increase the length by 2 mm is

Work done = fraction numerator 1 over denominator 2 end fraction blank F increment l
fraction numerator equals blank fraction numerator 1 over denominator 2 end fraction fraction numerator Y A increment l to the power of 2 end exponent over denominator l end fraction over denominator fraction numerator 2 cross times 10 to the power of 11 end exponent cross times 10 to the power of negative 6 end exponent open parentheses 2 cross times 10 to the power of negative 3 end exponent close parentheses to the power of 2 end exponent over denominator 2 cross times 1 end fraction end fraction open vertical bar table row cell Y equals fraction numerator F l over denominator A increment l end fraction end cell row cell o r blank F equals fraction numerator Y A increment l over denominator l end fraction end cell end table close
= 4cross times 10 to the power of negative 1 end exponent blank J equals 0.4 blank J

A wire left parenthesis Y equals 2 cross times 10 to the power of 11 end exponent N m to the power of negative 2 end exponent right parenthesis has length 1 m and cross-sectional area 1 m m to the power of negative 2 end exponent. The work required to increase the length by 2 mm is

physics-General
Work done = fraction numerator 1 over denominator 2 end fraction blank F increment l
fraction numerator equals blank fraction numerator 1 over denominator 2 end fraction fraction numerator Y A increment l to the power of 2 end exponent over denominator l end fraction over denominator fraction numerator 2 cross times 10 to the power of 11 end exponent cross times 10 to the power of negative 6 end exponent open parentheses 2 cross times 10 to the power of negative 3 end exponent close parentheses to the power of 2 end exponent over denominator 2 cross times 1 end fraction end fraction open vertical bar table row cell Y equals fraction numerator F l over denominator A increment l end fraction end cell row cell o r blank F equals fraction numerator Y A increment l over denominator l end fraction end cell end table close
= 4cross times 10 to the power of negative 1 end exponent blank J equals 0.4 blank J
General
physics-

The diagram shows a force-extension graph for a rubber band. Consider the following statements
I. It will be easier to compress this rubber than expand it
II. Rubber does not return to its original length after it is stretched
III. The rubber band will get heated if it is stretched and released
Which of these can be deduced from the graph

Area of hysterisis loop gives the energy loss in the process of stretching and unstretching of rubber band and this loss will appear in the form of heating

The diagram shows a force-extension graph for a rubber band. Consider the following statements
I. It will be easier to compress this rubber than expand it
II. Rubber does not return to its original length after it is stretched
III. The rubber band will get heated if it is stretched and released
Which of these can be deduced from the graph

physics-General
Area of hysterisis loop gives the energy loss in the process of stretching and unstretching of rubber band and this loss will appear in the form of heating
General
physics-

A wire of length Land radius a rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of same material but of length 2L and radius 2 a is stretched with a force 2F, the increase in its length will be

Young’s modulus Y equals fraction numerator F L over denominator A l end fraction
equals fraction numerator F L over denominator pi a to the power of 2 end exponent l end fraction
Since for same material Young’s modulus is same, i e comma
Y subscript 1 end subscript equals Y subscript 2 end subscript
orfraction numerator F L over denominator pi a to the power of 2 end exponent l end fraction equals fraction numerator open parentheses 2 F close parentheses left parenthesis 2 L right parenthesis over denominator pi open parentheses 2 a close parentheses to the power of 2 end exponent l ʹ end fraction
orl to the power of ´ end exponent equals l

A wire of length Land radius a rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of same material but of length 2L and radius 2 a is stretched with a force 2F, the increase in its length will be

physics-General
Young’s modulus Y equals fraction numerator F L over denominator A l end fraction
equals fraction numerator F L over denominator pi a to the power of 2 end exponent l end fraction
Since for same material Young’s modulus is same, i e comma
Y subscript 1 end subscript equals Y subscript 2 end subscript
orfraction numerator F L over denominator pi a to the power of 2 end exponent l end fraction equals fraction numerator open parentheses 2 F close parentheses left parenthesis 2 L right parenthesis over denominator pi open parentheses 2 a close parentheses to the power of 2 end exponent l ʹ end fraction
orl to the power of ´ end exponent equals l