Elastic Potential Energy

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

A force of $10 \mathrm{N}$ holds an ideal spring with a $20 \mathrm{N}/\mathrm{m}$ spring constant in compression. The potential energy stored in the spring is 

A wire loaded by a load $\mathrm{Mg}$ extends by $l$, mechanical energy stored in the wire is,

A wire of length $\text{'}L\text{'}$ suspended vertically from a rigid support is made to suffer extension $\text{'}l\text{'}$ in its length by applying a force $\text{'}F\text{'}.$ Then the work done is $\underline{ }$

When a $8 \mathrm{m}$ long wire is stretched by a load of $10 \mathrm{kg}.\mathrm{wt},$ it is elongated by $1.5 \mathrm{mm}.$ The energy stored in the wire in this process is _____$\left(\mathrm{g}=10 \mathrm{m}·{\mathrm{s}}^{-2}\right)$

A rod elongates by $l$ when a body of mass $\mathrm{M}$ is suspended from it. The work done is

$K$ is the force constant of a spring. The work done in increasing its extension from $l_1$ to $l_2$ will be

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?

$K$ is the force constant of a spring. The work done in increasing its extension from $l_1$ to $l_2$ will be

The ratio of elastic potential energy per unit volume for two wires made out of same material and having same length but diameter in the ratio $1:2$, when stretched by the same load is:

An ideal initially unstretched spring with spring constant $k$ is hung from the ceiling with a block of mass $M$ attached to its lower end. The maximum possible extension in the spring when the mass is released is ___

Lengths $L, 2L \mathrm{and} 3L$ and radii $R, 2R \mathrm{and} 3R$ of three wires of the same material (Young's modulus $Y$), respectively which are joined end to end with weight $\mathrm{w}$ is suspended as shown below. Find the elastic potential energy of the system neglecting the self-weight.

A catapult is made of rubber cord which is 42 cm long, with 6 m m diameter of cross-section and of negligble mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of $20{\mathrm{ms}}^{-1}$. Neglect the change in the area of crose-section of the cord while stretched. The Young's modulus of rubber is approx:

Two springs $\mathrm{P}$ and $\mathrm{Q}$ having stiffness constants ${\mathrm{K}}_1$ and ${\mathrm{K}}_2(<{\mathrm{K}}_1)$ respectively, are stretched equally. Then:

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

Initially, a block of mass $m$ is at rest on a frictionless floor and the spring is in a relaxed condition. One end of the spring is rigidly attached to the block and the other end is fixed to a wall. A constant force is applied on the block as shown in the figure. The maximum velocity of the block is

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

One end of a slack wire (Young's modulus, $Y$, length, $L$ and cross-sectional area, $A$) is clamped to a rigid wall and the other end to a block (mass $m$) which rests on a smooth horizontal plane. The block is set in motion with a speed, $v$. What is the maximum distance the block will travel after the wire becomes taut?