**Elasticity**

- This video introduces the concept of deformability of an object, moving away from the assumption of rigid bodies till now. All objects deform or have elasticity to a certain extent, ranging from perfectly elastic to perfectly inelastic.
- This video shows graphically the intermolecular forces of an object as the reason for its shape and elasticity.
- This video explains the stress and strain developed in an objected when subjected to external force. It also explains the law governing the stress and elasticity relationship called Hooke's law.
- This video graphically explains the validity of the Hooke's law for elastic region and relationship between stress and strain along with terms like yield stress, yield point, breaking stress and fracture point.
- This video explains in detail the different type of stress and strain like Normal or longitudinal stress, tensile stress, compressive stress, tangential or shearing stress, bulk stress, shearing strain and volume strain along with their equations using different modulus like shearing and bulk modulus.
- A wire can sustain the weight of a block of mass m kg before breaking. If the wire is cut into two equal parts, each part can sustain a weight of….?
- As shown in figure, a horizontal mass-less aluminium rod projects from a wall and an object of known mass is suspended from the end of the rod. The shear modulus of aluminium is given. Find the shearing stress on the rod and the vertical deflection of the end of the rod.
- Given is the Compressibility of water. Find the decrease in given volume of water when subjected to a given pressure.
- Three rods of lengths l1, l2 l3, cross sectional areas A1, A2, A3 and Young's modulus Y1, Y2, Y3 are joined in series to form a single rod as shown in figure. Find the total elongation of the rod when a tensile force F is applied to it.
- A composite rod is formed by placing a brass tube over a steel tube, as shown in the figure. If a force F is applied to the composite rod, find the stress in each of the tubes, and the effective Young's modulus of the composite rod.
- This video explains the elastic potential energy gained by an object and the work done when a force is applied on it.
- The rubber cord of a catapult has a given cross-sectional area and total un-stretched length. It is stretched and then released to project a pebble of given mass. Find the velocity of projection if the Young's modulus for rubber is known.
- This video explains the concept of Poisson's ratio which is the ratio of lateral strain to the longitudinal strain when an object is stretched.
- A bar made of material whose Young's modulus is equal to 'Y' and Poisson's ratio to 'σ' is subjected to the hydrostatic pressure 'P'. Find (a) the fractional decrement in its volume and (b) the relationship between the compressibility K and the elastic constants Y and σ.
- As shown In figure, the cross-sectional area of the wire connecting the two blocks is 'A' and its Young's modulus is 'Y'. Find the strain developed in the wire if the applied force F is equal to m2 g/2. Assume the wire to be light and the friction to be absent.
- As shown in figure, three blocks of equal mass are connected through wires 'A' and 'B' whose cross-sectional area and the Young's modules is known. Neglecting friction find the longitudinal strain in wires A and B.
- A sphere of a given radius and mass is attached to the lower end of a steel wire which is suspended from the ceiling of the room. When the sphere is set swinging as a simple pendulum, its lowest point just grazes the floor. Calculate velocity of the ball at its lowest position. Young's modulus of steel, un-stretched length and radius of wire are given.
- A solid sphere of radius R made of a material of bulk modules B is surrounded by liquid in a cylinder container. A mass-less piston of area A floats on the surface of the liquid. Find the fractional change in the radius of sphere (dR/R) when a mass M is placed on the piston to compress the liquid.
- Two rods of identical dimension, with Young's moduli Y1 and Y2 are joined end to end. The equivalent Young's modulus for the composite rod is…?
- A mass-less wire, consisting of three segments AB, BC and CD of given length joined together, is hanging vertically from a fixed support at 'A' as shown in figure. The cross section of the wire is uniform and a weight of given mass is hung from D. Calculate the displacements of the points B, C and D using the given data on Young moduli.
- A body of given mass is suspended from a steel wire of known radius. Find the maximum angle to which the wire can be deflected so that it does not break when the load passes through the mean position. Breaking stress of wire is given.
- A 2 kg mass is attached to one end of an elastic string of natural length 1.5 m whose other end is fixed at a point O as shown in figure. The Young's modulus of the string is such that the 2 kg mass hanging vertically would stretch the string by 3 cm. The mass is held at the point O and is allowed to fall vertically. Find how far below the point O will it come to rest.
- A light rod of given length is suspended from the ceiling horizontally by means of two vertical wires of steel and brass of equal length tied to its ends. Find out the position along the rod at which a weight may be hung to produce a) Equal stresses in both wires b) Equal strains in both wires. Young's modulus and cross sectional area of the steel and brass wire is given.
- A steel wire is clamped firmly at two points A and B which are at a distance apart and in the same horizontal plane. A body is hung from the middle point of the wire such that the middle point sags a certain distance lower from the original position. Calculate the mass of the body. Given the Young's modulus, diameter and length of wire.
- A bar of cross section A is subjected to equal and opposite tensile force F at its ends. Consider a plane through the bar making an angle θ with a plane at right angles to the bar. Find the Tensile and shearing stress at this plane and the angle at which these will be maximum.
- A ring made of lead, of given radius is rotated about a vertical axis passing through its center and perpendicular to its plane. Find the number of revolution per second at which this ring will rupture. The density and tensile strength of lead is given.
- A tapering wire of length 'l' and radii 'a' and 'b' is subjected to a stretching force F. Find the extension produced in the wire if its Young's modulus is Y.
- A horizontally oriented rod of length 2L is being rotated about vertical axis passing through its center. Find the following. (a) the minimum number of revolutions at which this rod will rupture (b) the total change in length of rod as a function of angular velocity The tensile strength and density of copper is Given.
- An iron rod of length l is hung from the ceiling by one of its ends. Find (a) the extension Δl in the length of the rod due to its own weight, and (b) the relative increase in its volume ΔV/V.