Elasticity

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What can be said about the bulk modulus of elasticity for different states of matter?

Ksolid = Kliquid = Kgas
Ksolid < Kliquid < Kgas
Ksolid, Kliquid, and Kgas are undefined
Ksolid > Kliquid > Kgas (correct)

Which type of modulus is involved in the stretching of a rope in a suspension bridge?

Modulus of rigidity
Shear modulus
Young's modulus (correct)
Bulk modulus

What happens to the metallic parts of machinery if they are subjected to a stress beyond their elastic limit?

They break apart
They become more elastic
They undergo permanent deformation (correct)
They become stronger

Why are bridges declared unsafe after long use?

Because of the loss of elastic strength (B) Signup and view all the answers

What is the maximum height of a mountain on earth limited by?

The elastic behaviour of the earth (C) Signup and view all the answers

What is the characteristic of the material of wire A?

It has the highest Young's modulus of elasticity (B) Signup and view all the answers

What is the condition for an appreciable change in longitudinal extension of an elastic material?

The material must be in the form of a long thin rod (D) Signup and view all the answers

What is the elongation of a uniform heavy rod of weight W, cross-sectional area A and length L, hung from a fixed support, neglecting lateral contraction?

WL / (2AY) (C) Signup and view all the answers

What is the strain produced in a uniform elastic string placed over a smooth horizontal surface, when a constant force F0 is applied?

F0 / (YS) (B) Signup and view all the answers

What is the elongation of a uniform rod of length L, with a mass per unit length  and area of cross-section A?

λL / (AY) (A) Signup and view all the answers

What is the unit of Young's modulus?

N/m² (C) Signup and view all the answers

What is the relationship between the interatomic distance and the interatomic force constant in a material?

The interatomic distance is inversely proportional to the interatomic force constant (A) Signup and view all the answers

What is the phenomenon where the strain lags behind the stress in a material?

Elastic hysteresis (C) Signup and view all the answers

What is the significance of the area of the hysteresis loop in a material?

It represents the energy lost as heat during loading and unloading (B) Signup and view all the answers

Which type of material would be suitable for making car tyres?

Material with a small hysteresis loop (D) Signup and view all the answers

What is the relationship between the angle of twist and the radius of the cylindrical shell?

The angle of twist is directly proportional to the radius. (B) Signup and view all the answers

What is the relationship between the torsional rigidity and the radius of the cylindrical shell?

Torsional rigidity is directly proportional to the fourth power of the radius. (D) Signup and view all the answers

What is the work done in twisting the cylinder through an angle θ?

W = (1/2)Cθ^2 (B) Signup and view all the answers

What is the condition for a hollow shaft to be stronger than a solid rod of the same length and mass?

The radius of the hollow shaft must be greater than the radius of the solid rod. (B) Signup and view all the answers

What is the relationship between the angle of twist and the shearing strain?

The angle of twist is directly proportional to the shearing strain. (D) Signup and view all the answers

Why is it beneficial to increase the depth of a beam rather than its breadth in construction of roofs and bridges?

To minimize the depression in the beam (B) Signup and view all the answers

What is the advantage of a hollow shaft over a solid shaft of the same mass, length, and material?

The hollow shaft has a greater torque required to produce a unit twist (A) Signup and view all the answers

What is the condition for the base of a mountain to be stable?

K > hρg (D) Signup and view all the answers

What is the expression for the depression in a beam with a circular cross-section?

δ = WL^3 / 12πr^4Y (D) Signup and view all the answers

Why is an I-shaped girder used to support a load in construction?

To minimize the depression in the beam (B) Signup and view all the answers

If a rod of length $l$ is twisted by an angle $\theta$ at one end, and the other end is fixed, what is the angle of twist at the joint?

$8\theta/9$ (B) Signup and view all the answers

A wire of radius $r$ and length $L$ is clamped at one end and twisted by an angle $\theta$ at the other end. What is the angle of shear?

$r\theta/L$ (D) Signup and view all the answers

Two wires of the same length $L$ and material have radii $r_1$ and $r_2$, respectively. If they are twisted by the same couple, what is the ratio of their angles of twist?

$r_2^2/r_1^2$ (B) Signup and view all the answers

A rod of length $L$ is twisted by a torque $\tau$ at one end, and the other end is fixed. What is the twist angle at the joint?

$\tau L/2\pi\eta$ (B) Signup and view all the answers

Two rods of the same material and length $L$ are twisted by the same angle at one end, but one has a radius $r_1$ and the other has a radius $r_2$. What is the ratio of their torques?

$r_1^2/r_2^2$ (A) Signup and view all the answers