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1.

Modulus of rigidity of a liquidA. infinityB. zeroC. unityD. some finite small non-zero constant value

Answer» Correct Answer - B
No frictional (viscous) force exists in case of ideal fluid, hence, tangential forces are zero so there is no stress developed.
2.

What is value of modulus of rigidity for a liquid?A. InfinityB. zeroC. unityD. some finite small non-zero constant value

Answer» Correct Answer - B
The frictional (visvous) force cannot exist in case of ideal fiuid
3.

An iron rod B of length 1 m and mass 1 kg is suspended with help of two wires as shwon in figure. The area of cross-section of iron wire is 0.3 `cm^(2)` and of copper wire is `0.6cm^(2)`. In the above question, if `Y_("iron"):Y_(Cu)=2:1`, then the ratio of extension produced in copper wire to iron wire isA. `1:1`B. `2:1`C. `1:2`D. `1:4`

Answer» Correct Answer - B
4.

An iron rod B of length 1 m and mass 1 kg is suspended with help of two wires as shwon in figure. The area of cross-section of iron wire is 0.3 `cm^(2)` and of copper wire is `0.6cm^(2)`. At what distance from iron wire a weight can be hung to produce equal stress in wires?A. 0.82 mB. 0.38 mC. 0.67 mD. 0.47 m

Answer» Correct Answer - C
5.

A rod of length `l`, mass `M`, cross section area `A` is placed on a rough horizonatal surface. A horizonatal force `F` is applied to rod as shwon in figure. The coefficient of fricition between rod and surface is `mu`, the Young, modulus of material of rod is `Y`. [Assume that fricition force is distributed uniformly on rod] The elongation in the rod if `F lt mu Mg` isA. ZeroB. `[(F- (mu Mg)/(2))/(2AY)]l`C. `(Fl)/(2AY)`D. None

Answer» Correct Answer - C
Then, `F-T - f_(1) = 0 & T = f_(2)`
where `f_(1) + f_(2) = f = F`
As friction force is distributed uniformly, `f_(1) = (fx)/(l)`
`rArr T = F - f_(1) = F (f xx x )/(l) = F [1 - (x)/(l)]`
Let `Delta (dx)` be the elongation in `dx` lenghth of rod
`Delta (dx)` be the elongation in `dx` lenghth of rod
`Delta (dx) = (Tdx)/(Ay) = (F(1 - (x)/(l))dx)/(AY)`
Total elongation,
`Delta L = int Delta (dx) = int_(0)^(1) (F)/(AY) (1 - (x)/(l))dx = (Fl)/(2YA)`
6.

The length of a wire under stress changes by `0.01%`.The strain produced isA. `1xx10^(-4)`B. `0.01`C. `1`D. `10^(4)`

Answer» Correct Answer - B
Strain `= (Delta l)/(l)`
7.

Two parallel and opposite forces each 5000 N are applied tangentially to the upper and lower faces of a cubical metal block of side 25 cm. the angle of shear is (The shear modulus of the metal is 80 Gpa)A. `10^(-4) rad`B. `10^(-5) rad`C. `10^(-6) rad`D. `10^(-7) rad`

Answer» Correct Answer - C
Here, F = 5000 N
`L = 25 cm = 25 xx 10^(-2)m`
`A= (25xx 10^(-2)m)^(2) = 625 xx 10^(-4)m^(2)`
`eta = 80 GPa = 80xx 10^(9) Pa`
Angle of shear, `theta =(F)/(A eta) = (5000)/(625 xx 10^(-4)xx80xx 10^(9)) = 10^(-6)rad`
8.

A wire gets elongated by 4 mm when a block of mass 2 kg is suspended from it. Now, the block is immersed in water, the wire contracts by 1 mm. Find the density of block when the density of water is `1000kg//m^(3)`.

Answer» Correct Answer - `4g//cm^(3)`
9.

A metallic rod undergoes a strain of `0.5%`. The energy stroed per unit volume isA. `0.5xx10^(4) Jm^(-3)`B. `0.5xx10^(5) Jm^(-3)`C. `2.5xx10^(5) J m^(-3)`D. `2.5xx10^(4) J m^(-3)`

Answer» Correct Answer - D
`U = (1)/(2)Y ("strain")^(2)`
10.

Which of the following is the graph showing stress-strain variation for elastomers ?A. B. C. D.

Answer» Correct Answer - C
11.

The wires `A` and `B` shown in Fig. are made of the same material and have radii `r_(A)` and `r_(B)`, respectively. The block between them has a mass `m`. When the force `F` is `mg//3`, one of the wires breaks. Then A. for `r_(1) = r_(2),2` should be broken before 1.B. for `r_(1)` less than `2r_(2),2` should be broken before `1`C. data is indufiicentD. for `r_(1) = 2r_(2)`, any of the two may break

Answer» Correct Answer - D
Stress for wire `1, S_(1) = (4Mg)/(3 xx pi r_(1)^(2))` and
stress for wire `2, S_(2) = (Mg)/(3 xx pi r_(2)^(2))`
for `r_(1) = r_(2), S_(1) = 4S_(2)`
`therefore` any of the two wires may break because stress is same
12.

STATEMENT - 1 : A metallic rod placed upon smooth surface is heated. The strain produced is ZERO. STATEMENT - 2 : Strain is non-zero only when stress is developed in the rod. STATEMENT - 3 : Two metallic rods of length `l_(1)` and `l_(2)` and coefficient of linear expansion `alpha_(1)` and `alpha_(2)` are heated such that the difference of their length ramains same at ALL termperatures Then `(alpha_(1))/(alpha_(2))=(l_(2))/(l_(1))`A. TTTB. FTFC. FFTD. FFF

Answer» Correct Answer - A
13.

The wires `A` and `B` shown in Fig. are made of the same material and have radii `r_(A)` and `r_(B)`, respectively. The block between them has a mass `m`. When the force `F` is `mg//3`, one of the wires breaks. Then A. `A` will break before `B` if `r_(A) = r_(B)`B. `A` will break before `B` if `r_(A) lt 2r_(B)`C. Either `A` or `B` may break if `r_(A) = 2r_(B)`D. The lengths of `A` and `B` must be known to predict which wire will break.

Answer» Correct Answer - A::B::C
stress in wire `VB = (mg+(mg)/(3)) (1)/(pir_(A)^(2))`
14.

A rod area of cross section A is being acted upon by two forces F - F as shown in figure. Consider a section ab of rod whose normal makes angle `theta` with horimontal. The shear stress upon this section is maximum when `theta=(180^(@))/(n)`. Find n.

Answer» Correct Answer - 4
15.

Two identical rods are pulled as shown in figure (1) and (2). The surface are smooth. If `Deltal_(1) and Deltal_(2)` are the elongations in two cases respectively, then find `(Deltal_(2))/(Deltal_(1))`.

Answer» Correct Answer - 2
16.

Find the change in density of water in occean at depth of `700m` below the surface. The denity of water at the surface is `1000kg//m^(3)` and the bulk modulus of water is `4.9xx10^(9) Nm^(-2)`A. `2.4kg//m^(3)`B. `3.4kg//m^(3)`C. `1.4kg//m^(3)`D. `4.4kg//m^(3)`

Answer» Correct Answer - C
`Delta rho (P rho)/(K), P = hdg`
17.

A lift is tied with thick iron wire and its mass is `1000kg`. If the maximum acceleration of the lift is `1.2ms^(2)` and the maximum stress of the wire is `1.4xx10^(8) Nm^(2)` what should be the minimum diameter of the wire?A. `10^(-2)m`B. `10^(-4)m`C. `10^(-6)m`D. `0.5xx10^(-2)m`

Answer» Correct Answer - A
Breaking stress `= (m(g+a))/(pi r^(2))`
18.

A steel wire of unifrom cross-section `1 mm^(2)` is heated to `70^(@)C` and strechted by tying it two ends rigidly. Calculate the change in tension on the wire when temperature falls form `70^(@)C` to `35^(@)C`A. `70N`B. `72N`C. `74N`D. `77N`

Answer» Correct Answer - D
`F = YA* Delta t`
19.

A wire elongastes by 1.0 mm when a load W ils hung from it. If this wire goes over a pulley and two weights W each are hung at the two ends the elongation of the wire will beA. zeroB. `l//2`C. `l`D. `2l`

Answer» Correct Answer - C
Same tension `e alpha F`
20.

On taking a solid rubber ball from the surface to the bottom of a lake `100m` deep, the reduction in volume is found to eb `0.5%` if the density of water si `10^(3) kgm^(-3)` and `g = 10 ms^(-1)`, find the bulk modulus of rubber.A. `1xx10^(8)Pa`B. `2xx10^(8)Pa`C. `4xx10^(8)Pa`D. `6xx10^(8)Pa`

Answer» Correct Answer - B
`K = (P)/((DeltaV)/(V)), P = hdg`
21.

What is the density of ocean water at a depth, where the pressure is 80.0 atm, given that its density at the surface is `1.03 xx 10^(3) kg m^(-3)`? Compressibilty of water `= 45.8 xx 10^(-11) Pa^(-1)`. Given 1 atm. =`1.013 xx 10^(5) Pa`.

Answer» Let the given depth be h.
Pressure at the given depth, p = 80.0 atm = `80xx1.01xx10^(5)` Pa
Density of water at the surface, `rho_(1)=1.03xx10^(3)"kg"" m"^(-3)`
Let `rho_(2)` be the density of water at the depth h.
Let `V_(1)` be the volume of water of mass m at the surface.
Let `V_(2)` be the volume of water of mass m at the depth h.
Let `DeltaV` be the change in volume.
`DeltaV=V_(1)-V_(2)`
`=m((1)/(rho_(1))-(1)/(rho_(2)))`
`therefore"Volumetric strain"=(DeltaV)/(V_(1))`
`=m((1)/(rho_(1))-(1)/(rho_(2)))xx(rho_(1))/(m)`
`therefore (DeltaV)/(V_(1))=1-(rho_(1))/(rho_(2))" "...(i)`
Bulk modulus, `B=(pV_(1))/(DeltaV)`
`(DeltaV)/(V_(1))=(P)/(B)`
Compressibity of water = `(DeltaV)/(V_(1))=(P)/(B)`
`(1)/(B)=45.8xx10^(-11)"Pa"^(-1)`
`therefore(DeltaV)/(V_(1))=80xx1.013xx10^(5)xx45.8xx10^(-11)=3.71xx10^(-3)" "...(ii)`
For equations (i) and (ii), we get:
`1-(rho_(1))/(rho_(2))=3.71xx10^(-3)`
`rho_(2)=(1.03xx10^(3))/(1-(3.71xx10^(-3)))`
`=1.034xx10^(3)"kg m"^(-3)`
Therefore, the density of water at the given depth (h) is `1.034xx10^(3)"kg m"^(-3)`.
22.

Estimate the change in the density of water in ocean at a depth fo `500m` below the surface. The density of water at the surface `= 1030 kgm^(-3)` and the bulk modulus of water `= 2.2xx10^(9) Nm^(-2)`A. `2.363 kg//m^(3)`B. `1.363 kg//m^(3)`C. `4.363 kg//m^(3)`D. `3.363 kg//m^(3)`

Answer» Correct Answer - A
`K = (P)/(-(DeltaV)/(V)), P = hdg, (Delta rho)/(rho) = -(Delta V)/(V)`
23.

The modulus of rigidly of a liquid isA. zeroB. `1`C. infinityD. some other finite value

Answer» Correct Answer - A
24.

Steel is preferred for making springs over copper becauseA. `Y` of steel is more than that of copper.B. steel is cheaperC. `Y` of copper is more than steelD. steel is less likely to be oxidised

Answer» Correct Answer - A
25.

Two idential solid balls, one of ivory and the other of wet caly, are dropped from the same height on the floor. Which one will rise to a greater height after striking the floor and why ?

Answer» Since, ivory ball is more elastic than wet-clay ball, therefore, ivory ball tries to regain its original shape quickly. Hence, more energy and momentum is transferred to the ivory ball in comparison to the wet clay ball and therefore, ivory ball will rise higher after striking the floor.
26.

Two idential solid balls, one of ivory and the other of wet caly, are dropped from the same height on the floor. Which one will rise to a greater height after striking the floor and why ?A. ivory ball will rise to a greater height than wet clay ball.B. ivory ball will rise to a lesser height than wet clay ball.C. both balls will rise to the same height.D. data is insufficient.

Answer» Correct Answer - A
As the ivory ball is more elastic than wet clay ball, therefore it will tend to regain its shape instantaneously after the collision: Hence, there will be a large energy and momentum transfer compared to the wet clay. Thus, the ivory ball will rise higher after the collision.
27.

In a human pyramid in a circus, the entire weight of the balanced group is supported by the legs of a performero who is lying on his back (as shown in Fig. 9.5). The combined mass of all the persons performing the act, and the tables, plaques etc. involved is 60 kg. Each thighbone (femur) of this performer has a length of 50 cm and an effective radius of 2.0 cm. Determine the amount by which each thighbone gets compressed under the extra load.

Answer» Total mass of all the performers, tables, plaques etc. = 280 kg
Mass of the performer = 60 kg
Mass supported by the legs of the performer at the bottom of the pyramid
= 280 – 60 = 220 kg
Weight of this supported mass
= 220 kg wt. = 220 `xx` 9.8 N = 2156 N.
Weight supported by each thighbone of the performer = ½ (2156) N = 1078 N.
From Table 9.1, the Young’s modulus for bone is given by
`Y=9.4xx10^(9)"N m"^(-2)`.
Length of each thighbone `L` = 0.5 m
the radius of thighbone = 2.0 cm
Thus the cross-sectional area of the thighbone
`A=pixx(2xx10^(-2))^(2)"m"^(2)=1.26xx10^(-3)"m"^(2)`
Using Eq. (9.8), the compression in each thighbone `(DeltaL)` can be computed as
`Delta L=[(FxxL)//(YxxA)]`
`" "=[(1078xx0.5)//(9.4xx10^(9)xx1.26xx10^(-3))]`
`" "=4.55xx10^(-5)"m" or 4.55xx10^(-3)"cm"`
This is a very small change! The fractional decrease in the thighbone is `DeltaL//L` = 0.000091 or 0.0091%.
28.

A bob of mass `10 kg` is attached to a wire `0.3 m` long. Its breaking stress is `4.8xx10^(7) N//m^(2)`. Then area of cross-section of the wire is `10^(-6) m^(2)`. What is the maximum angular velocity with which it can be rotated in a horizontal circle?A. `2 "rad"//s`B. `4 "rad"//s`C. `6 "rad"//s`D. `8 "rad"//s`

Answer» Correct Answer - B
`mr omega^(2)` = Breaking stress `x A`
29.

A pendulum bob of mass `m` hangs form a massless elastic string. The potential energy (elastic + gravitational) of the system (bob + string + earth) measured relative to the position of the bob corresponding to the normal length of the string is: (where `x` = static deformation (elongation) of the string.)A. `mgx`B. `-(1)/(2)mgx`C. `2mgx`D. `-mgx`

Answer» Correct Answer - B
Potential energy of bob `w.r.t` given refference `= -mgx`
elastic potential energy of spring `= (1)/(2) kx^(2)`
`= (1)/(2) (mg)/(x) xx x^(2) = (1)/(2) mgx`
Hence total potential energy of the system
`= -mgx + (1)/(2) mgx = - (1)/(2) mgx`.
30.

What percent of length of a wire will increses by applying a stress fo `1kg. Wt//mm^(2)` on it. `[Y = 1xx10^(11) Nm^(-2) "and" 1 kg wt = 9.8N]`A. `0.0078%`B. `0.0088%`C. `0.0098%`D. `0.0067%`

Answer» Correct Answer - C
`(e)/(l) xx 100 = (F)/(AY) xx 100`
31.

A simple pendulum is made by attaching `1Kg` bob to `5m` long copper wire of diameter `0.08cm` and it has a certatin period of oscillation and `10kg bob` is replaced by `kg bb` the change in time period is `(Y = 12.4xx10^(10) Nm^(-2))`A. `0.0035 sec`B. `4.4915 sec`C. `4.488 sec`D. `0.0021 sec`

Answer» Correct Answer - A
`T_(1) = 2pi sqrt((l + Delta l_(1))/(g))` and `T_(2) = 2pi sqrt((l + Delta l_(2))/(g)),Delta T = T_(2) - T_(1)`
32.

A Copper wire and steel of the same diameter and length are connected end to end and a force is applied, which stretches their combined length by 1 cm. The two wires will haveA. the same stress and strainB. the same strain but different stressesC. the same stress but different strainsD. different stress and strains

Answer» Correct Answer - C
33.

A wire fixed at the upper end stretches by length l by applying a force F. The work done in stretching isA. `F//2l`B. `Fl`C. `2Fl`D. `Fl//2`

Answer» Correct Answer - D
work done `= (1)/(2) "stress" xx "strain" xx "volume"`
34.

The diagram shows a forc-extension graph for a rubber band. Consider of 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 streched III. The rubber band will get heated id it is streched and realeased Which of these can be deduced from the graphA. `II` onlyB. `II` and `III`C. `I` and `III`D. `I` only

Answer» Correct Answer - A
35.

A load of 4.0 kg is suspended from a ceiling through a steel wire of length 20 mand radius 2.0 mm. It is found that the length of the wire increases by 0.031 mm as equilibrium is achieved. Find Young modulus of steel. Take `g=3.1pims^-2`

Answer» Correct Answer - `Y=("Stress")/("Strain")`
`rArr" "Y=2xx10^(12)N//m^(2)`
Hint : `Y=("Stress")/("Strain")`
36.

The linear strain in `x,y` and `z` direction are `e_(x),e_(y)` and `e_(z)` respectively. Then the volumetric strain is givne byA. `e_(x) e_(y) e_(z)`B. `e_(x) + e_(y) + e_(z)`C. `e_(z) = e_(x) e_(y)`D. `e_(z) = (e_(x) + e_(y))/(2)`

Answer» Correct Answer - B
37.

The substance which shows partically no ealstic after effect isA. copperB.  silverC. rubberD. quartz

Answer» Correct Answer - D
38.

Two bars `A` and `B` of circular cross section, same volume and made of the same material, are subjected to tension. If the diameter of `A` is half that of `B` and if the force applied to both the rod is the same and it is in the elastic limit, the ratio of extension of `A` to that of `B` will beA. `16`B. `8`C. `4`D. `2`

Answer» Correct Answer - A
`e = (FV)/(YA^(2)), V = "volume"`
39.

The average depth of indian Ocean is about 3000 m. The fractional compression, `(triangleV)/(V)` of water at the bottom of the ocean is (Given Bulk modulus of the water `=2.2xx10^9Nm^-2` and `g=10ms^-2`)

Answer» The pressure exerted by a 3000 m column of water on the bottom layer
`p=hrhog=3000" m"xx1000" kg m"^(-3)xx10" m s"^(-2)`
`" "=3xx10^(7)"kg m"^(-1)"s"^(-2)`
`" "=3xx10^(7)"N m"^(-2)`
Fractional compression `DeltaV//V`, is
`DeltaV//V="Stress"//B=(3xx10^(7)"N m"^(-2))//(2.2xx10^(9)"N m"^(-2))`
`" "=1.36xx10^(-2)` or 1.36%
40.

A solid sphere of radius R made of a material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless pistion of area A floats on the surface of the liquid. When a mass M is placed on the piston to compress the liquid the fractional change in the radius of the sphere, `deltaR//R`, is .............A. `Mg//2AK`B. `Mg//3AK`C. `Mg//AK`D. `2Mg//3AK`

Answer» Correct Answer - B
Bulk modulus,
`K = ("Stress")/("Volume strain") = (F//A)/(DeltaV//V) = (Mg//A)/(DeltaV//V)`
or `(DeltaV)/(V) = (Mg)/(AK)" "...(i)`
Volume of sphere, `V= (4)/(3) piR^(3)`
`therefore DeltaV = 4piR^(2)DeltaR thereforeR therefore (DeltaV)/(V) = (4piR^(2))/ ((4)/(3) piR^(3)) = 3(DeltaR)/(R)`
or `(Mg)/(Ak) =3 (DeltaR)/(R)`, from (i)
or ` (DeltaR)/(R) = (Mg)/(3AK)" "therefore" " (deltaR)/(R) = (Mg)/(3AK)`
41.

A solid sphere of radius R made of a material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless pistion of area A floats on the surface of the liquid. When a mass M is placed on the piston to compress the liquid the fractional change in the radius of the sphere, `deltaR//R`, is .............A. `(mg)/(AK)`B. `(mg)/(3AK)`C. `(mg)/(A)`D. `(3mg)/(AK)`

Answer» Correct Answer - B
`(DeltaV)/(V) = (F)/(AK) = (mg)/(AK), (Delta R)/(R) = (1)/(3) (Delta V)/(V)`
42.

A wire is suspended from the ceiling and stretched under the action of weight F suspended from its other end. The force exerted by the ceiling on it is equal and opposite to the weight.A. Tensile stress at any cross-section `A` of the wire is `F//A`.B. Tensile stress at any cross-section is zeroC. Tensile stress at any cross-section `A` fo the wrie is `2F//A`D. Tension at any cross-section `A` fo the wire is `F`.

Answer» Correct Answer - A::D
Force at each cross-section is `F`
Tension stress
`= ("Force applied")/("Area of cross-section") = (F)/(A)`
43.

A uniform pressure P is exerted by an external agent on all sides of a solid cube at temperature `t^(@)C`. By what amount should the temperature of the cube be raised in order to bring its volume back to its original volume before the pressure was applied if the bulk modulus is B and co-efficient of volumetric expansion is `gamma`?A. `(3P)/(K alpha)`B. `(P)/(2alpha K)`C. `(P)/(3alpha K)`D. `(P)/(alpha K)`

Answer» Correct Answer - C
`K = (P)/((DeltaV)/(V)), (Delta V)/(V) = gamma t = 3alpha t`
44.

When temperature of a gas is `20^@C` and pressure is changed from `p_(1)= 1.01 xx 10^(5) Pa` to `p_(2) = 1.165 xx 10^(5) Pa`, the volume changes by `10%`. The bulk modulus isA. `1.55xx10^(5)Pa`B. `0.115xx10^(5)Pa`C. `1.4xx10^(5)Pa`D. `1.01xx10^(5)Pa`

Answer» Correct Answer - A
`K = (Delta P)/(Delta V//V) = ((1.165-1.01)xx10^(5))/((10//100))`
`K = 1.55xx10^(5)` pascal
45.

The figure shows a horizontal block that is suspended by two wires A and B which are identical except their original length. Which wire was originally shorter? A. AB. BC. Both had equal lengthD. Any one of them could be shorter

Answer» Correct Answer - B
46.

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is appliedA. Length `= 50cm`, diameter `= 0.5mm`B. Length `= 100cm`, diameter `= 1mm`C. Length `= 200cm`, diameter `= 2mm`D. Length `= 300cm`, diameter `= 3mm`

Answer» Correct Answer - A
`F = (AY)/(l).(Delta l), Delta l = (F l)/(A.Y)`
`A = (pi D^(2))/(4), :. Delta l alpha (L)/(D^(2))`
Now for case `(a), (L)/(D^(2)) = 2xx10^(4)`
Thus, `(L)/(D^(2))` is maximum is case (a).
47.

On loading a metal wire of cross section `10^(-6) m^(2)` and length `2m` by a mass of `210kg`, it extends by `16mm` and suddenly broke form the point of support . If denstiy of that metal is `8000K gm^(-3)` and its specific heat is `420J Kg^(1) K^(-1)` the ride in temperature of wire isA. `2.5^(@)C`B. `5^(@)C`C. `6^(@)C`D. `10^(@)C`

Answer» Correct Answer - A
`Delta t = (Fe)/(2A L rho S)`
48.

The following four wires are made of the same material which of these will have the largest extension when the same tension is appliedA. Length 50 cm, diameter 0.5 mmB. Length 100 cm, diameter 1 mmC. Length 200 cm, diameter 2 mmD. Length 300 cm, diameter 3 mm

Answer» Correct Answer - A
49.

When a load W is hung from a wire, it extends by `Deltal`. The heat produced in the process isA. `W xx Deltal`B. `(1)/(2)Wxx Deltal`C. `(WxxDeltal)/(4)`D. Zero

Answer» Correct Answer - B
50.

Two wires of equal cross section but one made of steel and the other of copper, are joined end to end. When the combination is kept under tension, the elongations in the two wires are found to be equal. Find the ratio of the lengths of the two wires. Young modulus of steel `=2.0xx10^11Nm^-2` and that of copper `=1.1xx10^1Nm^-2`A. `20:11`B. `11:20`C. `5:4`D. `4:5`

Answer» Correct Answer - A
`(l_(s))/(l_(c)) (Y_(s))/(Y_(c)) `, in series, stress = constatn, `e = (FL)/(AY)`