Elastic Potential Energy

Q.

When a block of mass M is suspended by a long wire of length L, the length of the wire becomes L+l. The elastic potential energy stored in the extended wire is

1. Mgl
2. MgL
3. 1/2Mgl
4. 1/2MgL

Q.

What are the different types of work?

Q. A small block of mass $m$ is kept on a rough inclined surface of inclination $\theta$ fixed in an elevator. The elevator goes up with a uniform velocity $v$ and the block does not slide on the wedge. The work done by the force of friction on the block in a time $t$ will be

1. zero
2. $mgvt{\cos }^2\theta$
3. $mgvt{\sin }^2\theta$
4. $\frac{1}{2}mgvt\sin 2\theta$

Q. A particle of mass $5\times {10}^{-6}\text{g}$ is kept over a large horizontal sheet of charge density $4\times {10}^{-6}{\text{C/m}}^2$. What charge should be given to this particle so that if released, it remains in equilibrium? [Take ${ϵ}_0=9\times {10}^{-12}{\text{C}}^2{\text{/Nm}}^2$]

1. $2.3\times {10}^{-13}\text{C}$
2. $3.3\times {10}^{-13}\text{C}$
3. $4.6\times {10}^{-13}\text{C}$
4. $9.2\times {10}^{-13}\text{C}$

Q.

The potential energy of a strained body comes out to be ½ x stress x strain x volume.
Can you derive this relation?

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

1. $\frac{4mg}{k}$
2. $\frac{2mg}{k}$
3. $\frac{mg}{k}$
4. $\frac{mg}{2k}$

Q.

The friction coefficient between the horizontal surface and each of the blocks shown in figure (9-E20) is 0.20. The collision between the blocks is perfectly elastic. Find the separation between the two blocks when they come to rest. Take $g-10m/s^2.$

Q. Figure shows a spring fixed at the bottom end of an incline of inclination ${37}^{\circ }$. A small block of mass $2\text{kg}$ starts slipping down the incline from a point $5.8\text{m}$ away from the spring. The block compresses the spring by $20\text{cm}$, stops momentarily and then rebounds through a distance of $1\text{m}$ up the incline. The friction coefficient between the plane and the block and the spring constant of the spring is (Take $g=10{\text{m/s}}^2$)

1. $\mu =0.12,k=1032\text{N/m}$
2. $\mu =0.12,k=962\text{N/m}$
3. $\mu =0.28,k=962\text{N/m}$
4. $\mu =0.54,k=1032\text{N/m}$

Q.

A particle of mass$100g$ is thrown vertically upwards with a speed of $5$ m/s. The work done by the force of gravity during the time, the particle goes up is

1. $-0.5J$

2. $-1.25J$

3. $1.25J$

4. $0.5J$

Q.

What is the work done by the Earth in moving around the Sun?

Q. A spring of force constant 10 N/m has an initial stretch 0.20 m. In changing the stretch to 0.25 m, the increase in potential energy is about-

1. 0.3 J
2. 0.5 J
3. 0.1 J
4. 0.2 J

Q. A spring of unstretched length $l$ and force constant $k$ is stretched by a small length $x$. It is further stretched by another small length $y$. The work done in the second stretching is

1. $\frac{1}{2}k(x^2+y^2)$
2. $\frac{1}{2}ky(2x+y)$
3. $\frac{1}{2}k{x}^2$
4. $\frac{1}{2}kx(x+2y)$

Q.

.A block of mass 5.0 kg is suspended from the end of a vertical spring which is stretched by 10 cm under the load of the block. The block is given a sharp impulse from below so that it acquires an upward speed of 2.0 m/s. How high will it rise ? Take g = $10m/s^2$

Q.

Consider the situation shown in figure (8-E8). Initially the spring is unstretched when the system is released form rest. Assuming no friction in the pulley, find the maximum elongation of the spring.

Q.

A body of mass 0.1 kg moving with a velocity of 10 m/s hits a spring (fixed at the other end) of force constant 1000 N/m and comes to rest after compressing the spring. The compression of the spring is

1. 0.01 m

2. 0.1 m

3. 0.2 m

4. 0.5 m

Q. The capacitance of a parallel plate capacitor is $C_0$ when the plates have air between them. This region is now filled with a dielectric slab of dielectric constant $K$ and capacitor is connected with a battery of emf $E$ and zero internal resistance. Now slab is taken out, then during removal of slab:

$1.)$ Charge $E{C}_0(K-1)$ flows through the cell.

$2.)$ Energy $E^2{C}_0(K-1)$ is absorbed by cell.

$3.)$ The energy stored in the capacitor is reduced by $E^2{C}_0(K-1)$.

$4.)$ The external agent has to do $E^2{C}_0(K-1)$ amount of work to take out the slab.

Select the correct phenomenon happening during the process:

1. $1\&3$
2. $2\&3$
3. $2,3\&4$
4. $1\&2$

Q. A spring of natural length ${}^{\prime }{x}^{\prime }\text{m}$ is compressed to half of its length. If the force constant $k$ of spring is $6\text{N/m}$, then it's potential energy ($\text{joule}$) is:

1. $3x^2$
2. $\frac{2}{3}{x}^2$
   
3. $\frac{3}{4}{x}^2$
   
4. $6x^2$
   

Q.

A block of mass 250 g is kept on a vertical spring of spring constant 100 N/m fixed from below. The spring ' is a now compressed to have a length 10 cm shorter than . its natural length and the system is released from this position. how does the block rise ? Take $g=10m/s^2$

Q.

The potential energy of a long spring when stretched by $2\mathrm{cm}$ is U. If the spring is stretched by $8\mathrm{cm}$ the potential energy stored in it is:-

1. $4\mathrm{U}$

2. $8\mathrm{U}$

3. $16\mathrm{U}$

4. $\frac{\mathrm{U}}{4}$

Q.

Figure shows a smooth curved track terminating in a smooth horizontal part. A spring of spring constant 400 N/m is attached at one end to a wedge fixed rigidly with the horizontal part. A 40 g mass is released from rest at a height of 4.9 m on the curved track. Find the maximum compression of the spring. (g = 9.8 m/$s^2$)

1. 4.9 m

2. 4.6 m

3. 9.8 m

4. None of these

Q. A body of mass $m$ hangs by as inextensible light string that passes over a smooth massless pulley that is fitted with a light spring of stiffness $k$ as shown in the figure. If the body is released from rest, calculate the maximum elongation of the spring. Take $g=10{\text{m/s}}^2$.

1. $\frac{mg}{k}$
2. $\frac{2mg}{k}$
3. $\frac{4mg}{k}$
4. $\frac{3mg}{k}$

Q. A wire of initial length $L$ and radius $r$ is stretched by a length $l$. Another wire of same material but with initial length $2L$ and radius $2r$ is stretched by a length $2l$. The ratio of the stored elastic energy per unit volume in the first and second wire is

1. $1:4$
2. $1:2$
3. $2:1$
4. $1:1$

Q. The potential energy of a certain spring when stretched through a distance ‘S’ is 10 joule. The amount of work (in joule) that must be done on this spring to stretch it through an additional distance ‘S’ will be

1. 40
2. 10
3. 30
4. 20

Q. By inserting a plate of dielectric material between the plates of a parallel plate capacitor at a constant potential, the energy is increased five times. The dielectric constant of the material is

Q. Assertion : The direction of induced emf is alwayssuch as to oppose the change that causes it. Reason : Conservation of energy applies to know the direction of induced emf.

Q. Two blocks \(A\) and \(B, \) each of mass \(2~\text{kg}\) are connected to two identical springs of spring constant \(800~Nm^{-1}\) and are placed on a smooth horizontal surface as shown in the figure. Initially the springs are relaxed. Now, the block \(A\) is slightly displaced to left and block \(B\) to right by the same distance and then released simultaneously. If the resulting collision is elastic, the time period of oscillation of the system is . The value of \(n\) is \(\dfrac{\pi}{5 n} s.\) The value of \(n\) is

Q. A thin string is held at one end and oscillates vertically so that, y (x=0, t) = 8 sin 4t (cm). Neglect the gravitational force. The string passes through bath filled with 1 kg water. Due to friction, heat is transferred to the both. The heat transfer efficiency is 50%. Calculate how much time passes before the temperature of the bath rises by one degree kelvin.

1. 1.1 day
2. 2.5 day
3. 3.1 day
4. 4.2 day

Q. A $3\text{kg}$ block collides with a massless spring of spring constant $110\text{N/m}$ attached to a wall. The speed of the block was observed to be $1.4\text{m/s}$ at the moment of collision. The acceleration due to gravity is $9.8{\text{m/s}}^2$. How far does the spring compress if the horizontal surface on which the mass moves is frictionless?

1. $0.23\text{m}$
2. $2.5\text{m}$
3. $3.2\text{m}$
4. $0.41\text{m}$

Q. A spring block system is compressed $x\text{m}$ from the mean position and released. Find out the total work done by the spring force when it reaches the other extreme point (fully stretched). Neglect friction.

1. $\frac{1}{2}k{x}^2$
2. $k{x}^2$
3. $\frac{1}{2}k(2x{)}^2$
4. $0$

Q. A block is attached to a spring having equilibrium position at $x=0$. The block oscillates between $x=-4\text{m}$ and $x=4\text{m}$. Find the change in potential energy stored in the spring when the block moves from $x=2$ to $x=-3$. Given the spring constant is $5\text{N/m}$.

1. $32.5\text{J}$
2. $12.5\text{J}$
3. $37.5\text{J}$
4. $10\text{J}$