Elastic Energy

Which of the given metal is not using for making rope for the crane?

Find maximum height of mountain on earth's surface.

The buckling of a beam is found to be more if:

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?

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

Which of the following expressions can be used to calculate the maximum height of mountains on earth?

What can be the maximum height of a mountain on earth?

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:

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.

 Lengths L, 2L and 3L and radii R, 2R and 3R of three wires of same material (Young's modulus Y) respectively  which are joined end to end with weight $\omega$ is suspended as shown below. Find the elastic ${\left(P.E\right)}_{system}$  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:

A uniform rod of length $l$ is acted upon by a force $F$ in a gravity-free region, as shown in the figure. If the area of cross-section of the rod is $A$ and it's Young's modulus is $Y$, then the elastic potential energy stored in the rod due to elongation is

A wire, suspended vertically from one of its ends, is stretched by attaching a weight of $200 \mathrm{N}$ to the lower end. The weight stretches the wire by $1 \mathrm{m}\mathrm{m}$. If the elastic energy (in $\mathrm{J}$) stored in the wire is $U$, What is the value of $\frac{1}{U}$?

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

Which of the following statements is/are correct for mechanical standing wave on a stretched wire?

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