# Solved papers for JEE Main & Advanced Physics Elasticity JEE PYQ-Elasticity

### done JEE PYQ-Elasticity Total Questions - 32

• question_answer1) A wire fixed at the upper end stretches by length 1 by applying a force $F$. The work done in stretching is [AIEEE 2004]

A)
$\frac{F}{2l}$

B)
$Fl$

C)
$2Fl$

D)
$\frac{Fl}{2}$

• question_answer2) 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 [AIEEE 2005]

A)
$2{{S}^{2}}Y$

B)
$\frac{{{S}^{2}}}{2Y}$

C)
$\frac{2Y}{{{S}^{2}}}$

D)
$\frac{S}{2Y}$

• question_answer3) 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)                                                    [AIEEE 2006]

A)
$l$

B)
$2l$

C)
zero

D)
$l/2$

• question_answer4) Two wires are made of the same material and have the same volume. However wire 1 has cross-section area A and wire 2 has cross- sectional area 3A. If the length of wire 1 increases by$\Delta x$on applying force F, how much force is needed to stretch wire 2 by the same amount?                                                                                 [AIEEE 2009]

A)
F

B)
4F

C)
6F

D)
9F

• question_answer5) A structural steel rod has a radius of 10 mm and length of 1.0 m. A 100 kN force stretches it along its length. Young's modulus of structural steel is $2\times {{10}^{11}}N{{m}^{-2}}.$ The percentage strain is about [JEE ONLINE 07-05-2012]

A)
0.16%

B)
0.32%

C)
0.08%

D)
0.24%

• question_answer6)  The load versus elongation graphs for four wires of same length and made of the same material are shown in the figure. The thinnest wire is represented by the line [JEE ONLINE 07-05-2012]

A)
OA

B)
OC

C)
OD

D)
OB

• question_answer7) A steel wire can sustain 100 kg weight without breaking. If the wire is cut into two equal parts, each part can sustain a weight of                                                                                                  [JEE ONLINE 19-05-2012]

A)
50kg

B)
400kg

C)
100kg

D)
200kg

• question_answer8)  If the ratio of lengths, radii and Young module of steel and brass wires in the figure are a, b and c respectively, then the corresponding ration of increase in lengths is: [JEE ONLINE 09-04-2013]

A)
$\frac{3c}{2a{{b}^{2}}}$

B)
$\frac{2{{a}^{2}}c}{b}$

C)
$\frac{3a}{2{{b}^{2}}c}$

D)
$\frac{2ac}{{{b}^{2}}}$

• question_answer9) A uniform wire (Youngs modulus $2\times {{10}^{11}}{{\operatorname{Nm}}^{-2}}$) is subjected to longitudinal tensile stress of $5\times {{10}^{7}}{{\operatorname{Nm}}^{-2}}$. If the overall volume change in the wire is 0.02%, the fractional decrease in the radius of the wire is close to: [JEE ONLINE 22-04-2013]

A)
$1.0\times {{10}^{-4}}$

B)
$1.5\times {{10}^{-4}}$

C)
$0.25\times {{10}^{-4}}$

D)
$5\times {{10}^{-4}}$

• question_answer10) A copper wire of length 1.0 m and a steel wire of length 0.5 m having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by 1 mm. if the youngs modulii of copper and steel are respectively $1.0\times {{10}^{11}}{{\operatorname{Nm}}^{-2}}$ and $2.0\times {{10}^{11}}\,N{{m}^{-2}}$, the total extension of the composite wire is:    [JEE ONLINE 23-04-2013]

A)
1.75 mm

B)
2.0 mm

C)
1.50mm

D)
1.25 mm

• question_answer11)  Two blocks of masses m and M are connected by means of a metal wire of cross-sectional area A Passing over a frictionless fixed pulley as shown in the figure. The system is then released. If  $\operatorname{M}=2$ m, then the stress produced in the wire is:                        [JEE ONLINE 25-04-2013]

A)
$\frac{2\operatorname{mg}}{3A}$

B)
$\frac{4\operatorname{mg}}{3A}$

C)
$\frac{\operatorname{mg}}{A}$

D)
$\frac{3\operatorname{mg}}{4A}$

• question_answer12) In materials like aluminium and copper, the correct order of magnitude of various elastic modulii is:       [JEE ONLINE 09-04-2014]

A)
Youngs modulus < shear modulus < bulk modulus.

B)
Bulk modulus < shear modulus < Youngs modulus

C)
Shear modulus < Youngs modulus < bulk modulus.

D)
Bulk modulus < Youngs modulus < shear modulus

• question_answer13)  Steel ruptures when a shear of $3.5\times {{10}^{8}}N{{m}^{-2}}$is applied. The force needed to punch a 1 cm diameter hole in a steel sheet 0.3 cm thick is nearly: [JEE ONLINE 12-04-2014]

A)
$1.4\times {{10}^{4}}N$

B)
$2.7\times {{10}^{4}}N$

C)
$3.3\times {{10}^{4}}N$

D)
$1.1\times {{10}^{4}}N$

• question_answer14) A uniformly tapering conical wire is made from a material of Young's modulus Y and has a normal, un extended length L. The radii, at the upper and lower ends of this conical wire , have values R and 3R, respectively, The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower and The equilibrium extended length, of this wire, would equal                                                                                                          [JEE ONLINE 09-04-2016]

A)
$L\left( 1+\frac{1}{3}\frac{Mg}{\pi Y{{R}^{2}}} \right)$

B)
$L\left( 1+\frac{2}{3}\frac{Mg}{\pi Y{{R}^{2}}} \right)$

C)
$L\left( 1+\frac{1}{9}\frac{Mg}{\pi Y{{R}^{2}}} \right)$

D)
$L\left( 1+\frac{2}{9}\frac{Mg}{\pi Y{{R}^{2}}} \right)$

• question_answer15)  A bottle has an opening of radius a and length b. A cork of length b and radius $\left( a+\Delta a \right)$ where $\left( \Delta a< A) \[\left( 2\pi g\mu B\,\,b \right)\Delta a$

B)
$\left( \pi \mu B\,\,b \right)\Delta a$

C)
$\left( \pi \mu \,B\,\,b \right)a$

D)
$\left( 4\pi \mu \,B\,\,b \right)\Delta a$

• question_answer16) A thin 1m long rod has a radius of 5 mm. A force of $50\,\,\pi kN$ is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01 mm, which of the following statements is false?                                                                      [JEE ONLINE 10-04-2016]

A)
The maximum value of Y that can be determined is ${{10}^{14}}N/{{m}^{2}}$

B)
$\frac{\Delta Y}{Y}$gets minimum contribution from the uncertainty in the length.

C)
The figure of merit is the larges for the length of the rod.

D)
$\frac{\Delta Y}{Y}$ gets its maximum contribution from the uncertainty in strain.

• question_answer17) A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of:                                      [JEE Main 2017]

A)
81

B)
$\frac{1}{81}$

C)
9

D)
$\frac{1}{9}$

• question_answer18) An external pressure P is applied on a cube at $0{{\,}^{o}}C$so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and$\alpha$is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by:                                      [JEE Main 2017]

A)
$\frac{3\alpha }{PK}$

B)
$3PK\alpha$

C)
$\frac{P}{3\alpha K}$

D)
$\frac{P}{\alpha K}$

• question_answer19) A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, $\left( \frac{dr}{r} \right),$is:                                                                                  [JEE Main Online 08-04-2018]

A)
$\frac{\text{mg}}{\text{3}\,\,\text{Ka}}$

B)
$\frac{mg}{Ka}$

C)
$\frac{Ka}{mg}$

D)
$\frac{Ka}{3\,\,mg}$

• question_answer20)  As shown in the figure, forces of ${{10}^{5}}N$ each are applied in opposite directions, on the upper and lower faces of a cube of side$10cm$, shifting the upper face parallel to itself by$0.5cm$. If the side of another cube of the same material is $20cm$, then under similar conditions as above, the displacement will be: [JEE Online 15-04-2018 (II)]

A)
$1.00\,\,cm$

B)
$0.25\,\,cm$

C)
$0.37\,\,cm$

D)
$0.75\,\,cm$

• question_answer21) In a youngs double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength $\lambda \text{ }=\text{ }500\text{ }nm$ is incident on the slits. The total number of bright fringes that are observed in the angular range $-30{}^\circ \le \,\theta \le 30{}^\circ$ is: [JEE Main 09-Jan-2019 Evening]

A)
640

B)
641

C)
320

D)
321

• question_answer22) In a Youngs double slit experiment with slit separation 0.1 mm, one observes a bright fringe at angle $\frac{1}{40}$ rad by using light of wavelength${{\lambda }_{1}}$. When the light of wavelength ${{\lambda}_{2}}$ is used a bright fringe is seen at the same angle in the same set up. Given that ${{\lambda}_{1}}$ and ${{\lambda}_{2}}$ are in visible range (380 nm to 740 nm), their values are - [JEE Main 10-Jan-2019 Morning]

A)
400 nm, 500 nm

B)
625 nm, 500 nm

C)
380 nm, 500 nm

D)
380 nm, 525 nm

• question_answer23) A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in Searles apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of increase in length of the steel wire is-      [JEE Main 12-Jan-2019 Evening]

A)
4.0 mm

B)
zero

C)
5.0 mm

D)
3.0 mm.

• question_answer24) A boy's catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of $20m{{s}^{-1}}.$Neglect the change in the area of cross-section of the cord while stretched. The Young's modulus of rubber is closest to:                                         [JEE Main 8-4-2019 Morning]

A)
${{10}^{4}}\,N{{m}^{-2}}$

B)
${{10}^{8}}\,N{{m}^{-2}}$

C)
${{10}^{6}}\,N{{m}^{-2}}$

D)
${{10}^{3}}\,N{{m}^{-2}}$

• question_answer25) A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that $g=3.1\pi m{{s}^{-2}},$what will be the tensile stress that would be developed in the wire?         [JEE Main 8-4-2019 Morning]

A)
$4.8\times {{10}^{6}}\text{ }N{{m}^{2}}$

B)
$5.2\times {{10}^{6}}\text{ }N{{m}^{2}}$

C)
$6.2\times {{10}^{6}}\text{ }N{{m}^{2}}$

D)
$3.1\times {{10}^{6}}\text{ }N{{m}^{2}}$

• question_answer26) Young's moduli of two wires A and B are in the ratio 7 : 4. Wire A is 2 m long and has radius R. Wire B is 1.5 m long and has radius 2 mm. If the two wires stretch by the same length for a given load, then the value of R is close to :-                                                                                              [JEE Main 8-4-2019 Afternoon]

A)
1.9 mm

B)
1.7 mm

C)
1.5 mm

D)
1.3 mm

• question_answer27) The elastic limit of brass is 379 MPa. What should be the minimum diameter of a brass rod if it is to support a 400 N load without exceeding its elastic limit?                                                 [JEE Main 10-4-2019 Afternoon]

A)
1.16 mm

B)
0.90 mm

C)
1.36 mm

D)
1.00 mm

• question_answer28) In an experiment, bras and steel wires of length 1m each with areas of cross section $1m{{m}^{2}}$are used. teh wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of 0.2 mm is : (Given, the Young's Modulus for steel and brass are respectively, $120\times {{10}^{9}}\text{ }N/{{m}^{2}}$ and $60\times {{10}^{9}}\text{ }N/{{m}^{2}}$)                                                   [JEE Main 10-4-2019 Afternoon]

A)
$0.2\times {{10}^{6}}\text{ }N/{{m}^{2}}$

B)
$4.0\times {{10}^{6}}\text{ }N/{{m}^{2}}$

C)
$1.8\times {{10}^{6}}\text{ }N/{{m}^{2}}$

D)
$1.2\times {{10}^{6}}\text{ }N/{{m}^{2}}$

• question_answer29) In a Young's double slit experiment, the ratio of the slit's width is 4:1. The ratio of the intensity of maxima to minima, close to the central fringe on the screen, will be :                                         [JEE Main 10-4-2019 Afternoon]

A)
${{(\sqrt{3}+1)}^{4}}:16$

B)
$9:1$

C)
$4:1$

D)
$25:9$

• question_answer30) A uniform cylindrical rod of length L and radius r, is made from a material whose Young's modulus of Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net longitudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equals to : [JEE Main 12-4-2019 Afternoon]

A)
$F/(3\pi {{r}^{2}}YT)$

B)
$3F/(\pi {{r}^{2}}YT)$

C)
$6F/(\pi {{r}^{2}}YT)$

D)
$9F/(\pi {{r}^{2}}YT)$

• question_answer31) A body of mass m = 10 kg is attached to one end of a wire of length 0.3 m. The maximum angular speed (in rad ${{s}^{-1}}$) with which it can be rotated about its other end in space station in (Breaking stress of wire =$4.8\text{ }\times \text{ }{{10}^{7}}\text{ }N{{m}^{2}}$ and area of cross-section of the wire = ${{10}^{2}}\text{ }c{{m}^{2}}$) is                                     [JEE MAIN Held on 09-01-2020 Morning]

• question_answer32) Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is [JEE MAIN Held on 09-01-2020 Evening]

A)
$\sqrt{2}:1$

B)
$2:1$

C)
$1:\sqrt{2}$

D)
$1:2$