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Correct answer is (B) False

Easiest explanation: A solid body which partially regains its SHAPE after complete removal of force is CALLED partially ELASTIC body. It is called COMPLETELY elastic when it completely regains its shape.

Correct OPTION is (a) Toughness

To EXPLAIN: Area under the stress-STRAIN curves represents toughness. Total deformation is given by the NET strain multiplied by original length. Modulus of ELASTICITY is the ratio of stress to strain under elastic limit.

Right ANSWER is (a) It breaks SOON after elastic limit is crossed

Easiest EXPLANATION: Brittle MATERIALS break soon after elastic limit. They show no significant plastic deformation and HENCE can’t be used for making wires. Their stress-strain curve looks like:

Correct choice is (b) False

For explanation: Stress can act along any direction to a PLANE. If it is PARALLEL to the plane it is called shearing stress & if it is perpendicular to the plane it’s called NORMAL stress. Pressure is always perpendicular to a unit area.

Right option is (d) Volumetric stress

For EXPLANATION: Volumetric stress is due to forces APPLIED on the surface of a body from all directions such force is along normal at each point. This causes a change in volume while mass, OBVIOUSLY, remains the same. So, there is a slight change in DENSITY. NOTE that it is negligible but this change of density doesn’t occur in any other type of stresses, as the change in longitudinal length is compensated by change in lateral length in case of longitudinal stresses.

Right choice is (a) True

The best explanation: Strain is DEFINED as change in length or volume divided by initial length or volume respectively. There can be cases when length or volume DECREASES LIKE when rod is compressed or body is inserted in fluid (it volume decreases due to pressure from all SIDES). Hence, strain can be negative.

Right answer is (C) Bsolid > Bliquid > Bgas

To ELABORATE: Bulk modulus is the inverse of compressibility. Solids are the least compressible, FOLLOWED by liquids and then gases being the most compressible. THUS solids have the maximum B, and liquids the least.

Right choice is (B) ΔV/V

To explain I WOULD SAY: The volumetric strain is defined as ratio of CHANGE in volume to original volume. It can be either positive or negative. The option -P / (ΔV/V) is the bulk modulus which is basically the ratio of volumetric stress to volumetric strain.

The CORRECT OPTION is (a) True

To explain: The stress strain CURVE of some elastic tissues of our bodies look similar to the curve represented by equation y = x^2. For EG, the elastic tissue of aorta has a curve like:

Correct OPTION is (a) 2.5*10^-3

For explanation I would SAY: PRESSURE at the bottom ‘P’ = ρgh = 1000*10*500 = 5*10^6Pa.

B = -P/(ΔV/V)

∴ ΔV/V = -P/B = 5*10^6/2*10^9 = 2.5*10^-3.

The correct OPTION is (b) (AY/L)xdx

For explanation I WOULD say: The force F at any instant will be EQUAL to internal force developed as the wire is to be slowly stretched.

∴ F=(AY/L)x

∴ Work done for dx EXTENSION = F*dx = (AY/L)xdx.

Right option is (c) 6.36*10^-7m

Explanation: The INITIAL length of wire is VOL / πr^2= 7.85*10^-5/ π*0.005^2 = 1m.

Stress = Y*strain. F/A = Y*Δl / l.

Δl = F/A * l/Y= (5/πr^2)*(1/10^11)

= 6.37*10^-7m.

Correct answer is (b) False

Explanation: Bulk modulus is defined as the ratio of volumetric stress to volumetric strain. And volumetric stress is force APPLIED per unit area which is pressure. Now, when pressure is applied on a body its volume DECREASES, therefore a minus sign is used to make bulk modulus POSITIVE. Hence, it is positive.

Right choice is (c) 1.98*10^-10

Best explanation: Bulk MODULUS ‘B’ is defined as -P / (ΔV/V). And B is the RECIPROCAL of compressibility.

∴ B = 1/10^-11= 10^11N/m^2.

 ΔV/V = P/B.

P = 10/(4π*0.04)

∴ ΔV/V = -P/B = – 10/(4π*0.04*10^11) = 1.98*10^-10.

Right choice is (a) ENERGY per unit VOLUME

Best explanation: Modulus of ELASTICITY is the ratio of stress to STRAIN. Its unit is, therefore, N/m^2. Energy per unit volume has the unit Nm/m^3 = N/m^2. FORCE per unit length has the unit N/m. So, the correct answer is energy per unit volume.

Right answer is (c) stress is proportional to strain under elastic limit

To EXPLAIN: Hooke’s LAW states that when DEFORMATION is small, stress is proportional to strain for ALMOST all materials. The region where this law is followed is SAID to be under elastic limit.

Correct option is (B) False

Explanation: Hooke’s law STATES that stress is proportional to strain under elastic limit. There are a few materials like elastomers which don’t FOLLOW hooke’s law. There are very few EXAMPLES like these in NATURE.

The correct CHOICE is (a) 0.4μm

Explanation: Tension ‘T’ in string will be GIVEN by T = mv^2/R = 1*4/0.1 = 40N.

Stress = Y*STRAIN, where Y is young’s modulus. T/A=Y*ΔL/L

∴ ΔL = TL/AY = (40*0.1)/(0.0001*10^11)

= 4*10^-7m = 0.4μm.

Correct option is (B) BREAKING stress

The explanation: Breaking stress refers to the stress at which the material FRACTURES. Ultimate stress is the maximum stress a material can handle before breaking. The material doesn’t FRACTURE at this stress. Yield stress refers to the stress after which PLASTIC deformation begins.

The correct answer is (a) Steel > Glass > Rubber

Easiest explanation: Elasticity is the PROPERTY of a material to regain shape when deforming FORCES are REMOVED. Out of the three, for the same stress, steel will SHOW MUCH less or maybe no permanent deformation as compared to glass which in turn will show less permanent deformation than rubber. Remember all this comparison is for the same amount of stress.

The correct choice is (a) Large DEFORMATION takes place between elastic limit and FRACTURE point

The explanation is: DUCTILE materials are those which can be drawn into wires as they deform by a significant amount between elastic limit and fracture point. The stress-strain CURVE of a ductile MATERIAL looks like: