Strain Energy

A work of$2\times {10}^{-2} \mathrm{J}$ is done on a wire of length $50 \mathrm{cm}$ and area of cross-section $0.5 {\mathrm{mm}}^2$. If the Young's modulus of the material of the wire is $2\times {10}^{10} \mathrm{N} {\mathrm{m}}^{-2}$, then the wire must be

When a steel wire fixed at one end is pulled by a constant force $F$ at its other end, its length increases by $l$. Which of the following statements is not correct?

When an elastic material with Young's modulus $E$ is subjected to a stretching stress $S,$ the elastic energy stored per unit volume of the material is

Show that strain energy per unit volume of a strained wire is $\frac{1}{2}\times stress\times strain$.

Write an expression for strain energy in a strained wire.

When the load on a wire is increased from $3 \mathrm{kg} \mathrm{wt}$ to $5 \mathrm{kg} \mathrm{wt}$ the elongation increases from $0.61 \mathrm{mm}$ to $1.02 \mathrm{mm}$. The required work done during the extension of the wire is

An elastic string of length $\mathrm{42\; cm}$  and cross section area ${10}^{-4}{\text{ m}}^2$ is attached between two pegs at a distance of $\mathrm{6\; mm}$. A particle of mass $50 \mathrm{g}$ is kept at mid point of string and stretched by $\mathrm{20\; cm}$ and released. As string attains natural length, the particle attains a speed $20\text{m}/\text{s}$. Then young’s modulus of string is of order

Work done for a certain spring when stretched through 1 mm is 10 joule. The amount of work that must be done on the spring to stretch it further by 1 mm is

Two wires of the same material and length but diameters in the ratio 1 : 2 are stretched by the same force. The elastic potential energy per unit volume for the wires, when stretched by the same force will be in the ratio.

The potential energy U between two atoms in a diatomic molecules as a function of the distance x between atoms has been shown in the figure. The atoms are

Consider four steel wires of dimensions given below (d = dimeter and l = length):

I. $\mathrm{l}=1\mathrm{m},\mathrm{d}=1\mathrm{m}\mathrm{m}$

II. $\mathrm{l}=2\mathrm{m},\mathrm{d}=2\mathrm{m}\mathrm{m}$

III. $\mathrm{l}=2\mathrm{m},\mathrm{d}=1\mathrm{m}\mathrm{m}$

IV. $\mathrm{l}=1\mathrm{m},\mathrm{d}=2\mathrm{m}\mathrm{m}$

If same force is applied to all the wires then the elastic potential energy stored will be maximum in wire.

A wire fixed at the upper end stretches by length, $L$ by applying a force, $F$. What is the work done in stretching the wire?

In a wire stretched by hanging a weight from its end, the elastic potential energy per unit volume in terms of longitudinal strain $\sigma$ and modulus of elasticity $Y$ is -

An elastic wire is stretched by $3 \mathrm{cm}$ from its natural length and its potential energy is $\mathrm{V}$. If the wire is stretched by $6 \mathrm{cm}$ from its natural length, its potential energy will be

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

A metal rod of Young's modulus $2\mathrm{ }\times \mathrm{ }{10}^{10}\mathrm{ }{\mathrm{N}\mathrm{m}}^{–2}$ undergoes an elastic strain of $0.06\%$. The energy per unit volume stored in $\mathrm{J}\mathrm{ }{\mathrm{m}}^{–3}$ is -

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

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

A metal rod of Young's modulus $2\times {10}^{10}\mathrm{ }{\mathrm{N}\mathrm{m}}^{-2}$ undergoes an elastic strain of $0.06\mathrm{\%}$. The energy per unit volume stored in $\mathrm{J}\mathrm{m}-3$ is -

The rubber cord catapult has a cross-section area $1\mathrm{ }{\mathrm{m}\mathrm{m}}^2$ and total unstretched length $10\mathrm{ }\mathrm{c}\mathrm{m}$. It is stretched to $12\mathrm{ }\mathrm{c}\mathrm{m}$ and then released to project a stone of mass $5\mathrm{ }\mathrm{g}\mathrm{m}$. Taking Young's modulus $\mathrm{Y}$ of rubber as $5\times {10}^8\mathrm{ }\mathrm{N} {\mathrm{m}}^{-2}$, the velocity of projection will be -