Elastic Potential Energy

The material commonly used for crane hooks is_____.

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

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

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 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?

 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

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

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?

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.

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