Elastic Potential Energy

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

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

The length of a wire is $1.0 \mathrm{m}$ and the area of cross-section is $1.0\times {10}^{-2} {\mathrm{cm}}^2$. If the work done for increase in length by $0.2 \mathrm{cm}$ is $0.4$ joule, then Young's modulus of the material of the wire is

Two wires of the same material and length, having diameters in the ratio $2 : 1,$ are stretched by the same force. The potential energy per unit volume stored in the two wires will be in the ratio:-

A wire of area of cross-section $3 {\mathrm{mm}}^2$ and natural length $50 \mathrm{cm}$ is fixed at one end and a mass of $2.1 \mathrm{kg}$ is hung from other end. Find the elastic potential energy stored in the wire in steady state.
$\left[\mathrm{Y}=1.9\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}\right]$

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

Load on a wire is increased from $3 \mathrm{kg}$ to $5 \mathrm{kg}$ due to which the elongation increases from $0.61 \mathrm{mm}$ to $1.02 \mathrm{mm}$. What was the work done during this increase in elongation?

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:

A pulling force is applied on a wire of Young's modulus $1.5\times {10}^{12} \mathrm{N}{\mathrm{m}}^{-2}$ so as to produce a strain of $2\times {10}^{-4}.$ The energy stored per unit volume is

Find the work done during the extension when the load on wire is slowly increased from $20 \mathrm{N}$ to $40 \mathrm{N}$ and the elongation from $0.6 \mathrm{mm}$ to $1.0 \mathrm{mm}$.

What will be the elastic energy stored in the wire which is suspended vertically from one of its ends is stretched by attaching a block of mass $200\mathrm{kg}$ to the lower end? The weight stretches the wire by $1 \mathrm{mm}$.

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:

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

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