Definition And Proof Based Problems

Q 3165801765

(i) Prove that the work done in stretching a wire per unit volume is `1/2 xx` tension `xx` extension

(ii) Prove that the work done per unit volume in stretching a wire for every type of strain `= 1/2 xx` stress `xx` strain.

(ii) Prove that the work done per unit volume in stretching a wire for every type of strain `= 1/2 xx` stress `xx` strain.

`(i) text(Work done)/(volume) = (1F)/(2L) . (Deltal)/(l)`

`:.` Work done 1`/2 F xx A (Deltal)/(l)`

`= 1/2` Tension x extension

(ii) The wire has length l, area of crosssection A made of material constant Y. Let a force F be applied and at any instance, x be the extension associated `(x < L),` where L is the maximum extension . At this instant , `F = (AY.x)/(l)`

Since force is a variable with `x`, Work done to stretch is,

`W = int_(0)^(L) Fdx`

`W= 1/2 (AY)/l . L^2`

`W = 1/2 (Al)((Y.L))/(l) (L/l)`

`=1/2` x Volume x Stress x Strain

`:.` Work done per unit volume

`= 1/2` Stress `xx` Strain

Q 3164591455

Explain the terms : Young's modulus of elasticity and elastic fatigue.

Young's modulus of elasticity is the ratio of the longitudinal stress to the longitudinal strain.

`Y = ((F/a)/(Deltal)/(l))` Elastic fatigue is the delay in getting back to the original status when the

deforming force is removed.

Q 3184591457

Give the similarities and differences between intermolecular and interatomic forces.

Similarities :

(i) Electrical by nature.

(ii) Active over short distances.

Differences :

(i) Force between molecules or atoms.

(ii) Molecular forces are weaker than interatomic forces.

Q 3134391252

What does Hooke's law essentially define ?

Elastic limit.

Q 3134491352

What do you mean by the elastic limit ?

When the deforming force is increased, a limit is reached beyond which the solid does not come back to its original shape or size but remains deformed on removal of applied force. This limit is called the elastic limit.

Q 3114280150

What are the factors that may affect elasticity of a material ?

It is a material constant. So all the physical quantities that might alter the nature like density can alter it.

Q 3174491356

Plot Load vs Extension curve for a metal on the graph and depict :

(i) Yield point, (ii) Breaking point, (iii)

Elastic limit, (iv) Crushing point

(i) Yield point, (ii) Breaking point, (iii)

Elastic limit, (iv) Crushing point