Elastic Potential Energy

A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is $600 \times 10^{-6}\text{ m}^3$. The elastic potential energy stored in the wire in stretched condition would be ______ J.

(Given Young modulus of copper $= 1.1 \times 10^{11}\text{ N/m}^2$)

A steel wire of length 2 m and Young's modulus $2.0 \times 10^{11}\text{ N m}^{-2}$ is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and $10^{-3}$ respectively, then the elastic potential energy density of the wire is __________ $\times 10^{5}$ (in SI units).

The amount of elastic potential energy per unit volume (in SI unit) of a steel wire of length $100\text{ cm}$ to stretch it by $1\text{ mm}$ is (if Young's modulus of the wire $= 2.0 \times 10^{11}\text{ Nm}^{-2}$):

An aluminium rod with Young's modulus $Y = 7.0 \times 10^{10}\text{ N/m}^2$ undergoes elastic strain of $0.04\%$. The energy per unit volume stored in the rod in SI unit is:

The elastic potential energy stored in a steel wire of length $20\text{ m}$ stretched through $2\text{ cm}$ is $80\text{ J}$. The cross sectional area of the wire is __________ $\text{mm}^2$.

$($ Given, $Y = 2.0 \times 10^{11}\text{ Nm}^{-2})$

The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of 5 $\times$ 10−4 is __________ kJ/m3. Assume that material is elastic upto the linear strain of 5 $\times$ 10−4.

A stone of mass 20 g is projected from a rubber catapult of length 0.1 m and area of cross section 10−6 m2 stretched by an amount 0.04 m. The velocity of the projected stone is ______________ m/s. (Young's modulus of rubber = 0.5 $\times$ 109 N/m2)

A metal rod has length, cross-sectional area and Young's modulus as $L, A$ and $Y$, respectively. If the elongation in the rod produced is $\ell$, then work done is proportional to

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:

A wire of length ' $L$ ' and area of cross section ' $A$ ' is made of material of Young's modulus ' $Y$. It is stretched by an amount ' $x$ '. The work done in stretching the wire is

When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L + $l$). The elastic potential energy stored in the extended wire is:

Work done in stretching a wire through 1 mm is 2 J. What amount of work will be done for elongating another wire of same material, with half the length and double the radius of cross section, by 1 mm?

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 20 ms–1. Neglect the change in the area of cross-section of the cord while stretched. The Young's modulus of rubber is closest to:

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

A wire fixed at the upper end stretches by length $l$ by applying a force $F.$ The work done in stretching is

A wire suspended vertically from one of its ends is stretched by attaching a weight of $200\text{ N}$ to the lower end. The weight stretches the wire by $1\text{ mm.}$ Then the elastic energy stored in the wire is