Elastic Potential Energy

Q. A ladder rests against a frictionless vertical wall, with its upper end 6m above the ground and the lower end 4m awayfrom the wall.The weight of the ladder is 500N and its C.G. at 1/3rd dis†an ce from the lower end.What will be the walls reaction in newton?

Q. If two springs $S_1$ and $S_2$ of force constants $k_1$ and $k_2$ respectively, are stretched by the same force, it is found that more work is done on spring $S_1$ than on spring $S_2$.

Statement-1: If stretched to the same extension, work done on $S_1$, will be more than that on $S_2$

Statement-2: $k_1<k_2$

Choose the correct option.

1. Statement-1 is true, Statement-2 is true and Statement-2 is not the correct explanation of Statement-1
2. Statement-1 is false, Statement-2 is true
3. Statement-1 is true, Statement-2 is false
4. Statement-1 is true, Statement-2 is true and Statement-2 is the correct explanation of statement-1.

Q.

A mass of 0.5 kg is suspended from a wire, then the length of the wire increases by 3 mm then work done is?

Q.

A block of mass 2.0 kg, initially at rest is pulled up on a smooth incline of angle 30⁰ with the horizontal. If the block moves with an acceleration of 1.0 m/s², find the power delivered by the pulling force at a time 4.0 s after the motion starts. What is the average power delivered during the 4.0 s after the motion starts?

1. None of these

2. 47 W, 24 W

3. 94 N, 48 N

4. 23 N, 12 N

Q. 40.A person of mass m is standing on one end of a plank of mass M and length L and floating in water. The person moves from one end to another and stops. Work done by normal force is

Q. 11. Force constants K, and K, of two springs are in the ratio 5 :4. They are stretched by same length. If potentialenergy stored in one spring is 25 J then potential energy stored in second spring is

Q. when a small mass m is suspended at lower end of an elastic wire having upper end fixed with ceiling .there is loss in gravitational potiential energy , let it be x, due to extension of wire , mark the correct option (1) the lost energy can be recovered (2) the lost energy is irrecoverable (3) Only x/2 amount energy is recoverable (4) Only x/3 amount of energy is recoverable

Q. A force of 100 N needs to be applied parallel to a smooth inclined plane just to hold a body on it. The angle of inclination of the inclined plane is ${30}^o$. How much horizontal force need to be applied to do the same?

1. 50N

2. 87N

3. 100N

4. 115N

Q. ring of mass m and radius R is pivoted at a point on its periphery. It oscillates with time period T. If a point mass m is gently attached at lowest point, then new time period is

Q. A weight mg is suspended from a spring. If the energy stored in the spring is U. The elongation in the spring is

Q.

A spring is cut in two halves. The spring constant of each half becomes

1. k²

2. Remain same

3. 2k

4. 1/2 k

Q.

A block of mass $m$ is attached rigidly with a light spring of force constant $k$. The other end of the spring is fixed to a wall. If block is displaced by a distance $x$, find the work done on the block by the spring for this range. (The spring force is given by $F=-kx$ , where $k$ is spring constant and $x$ is displacement of the block.)

1. 

2. 

3. 

4. 

Q. 66.For thhe path PQR in a conservative force field the amounts work done in carrying a body from P to Qand from Q toR are 5J and 2J respectively.The work done in carrying the body frim P to R will be - (1) 7J (2) 3J (3) \sqrt{}21J (4) zero

Q.

A wire suspended vertically from one of Its ends is stretched by attaching a weight of $\text{200}$N to the Lower End. The weight stretches the wire by $1$mm. Then the elastic energy stored in the wire is ?

Q. Three springs of constants k1, k2 and k3 are used to hang a mass m from the roof. The elastic potential energy stored in the array is

Q. a wire 2m in length suspended vertically stretches by 10mm when a mass of 10kg is attached to its lower end . the elastic potential gain by the wire is

Q. A wire of length 4 metre is hanging vertically from ceiling . If it is stretched due to its own weight find out energy stored per unit volume if Y=2×10^7 and density=10^3 kg/m^3

Q. ChoosecorrectA force of 10 N is applied on a 5 kg mass at rest.The work done by the force in first two second1.will be(1) 20 J(2) 40 J(4) ZeroPAJ(3) 30 J

Q. When a block a mass M is suspended by a long wire of length L, the elastic potential potential energy stored in the wire is $\frac{1}{2}$ × stress × strain × volume. Show that it is equal to $\frac{1}{2}$ Mgl, where l is the extension. The loss in gravitational potential energy of the mass earth system is Mgl. Where does the remaining $\frac{1}{2}$ Mgl energy go?

Q. a spring of negligible mass having a force constant k extends by an amount y when a mass m is hung from it. the mass is pulled down a little and then released. the system begins to execute SHM of amplitude A and angular frequency w. the total energy of the mass spring system will be

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 ?

Q. A body of mass 3 kg is under a force which causes a displacement in it is given by S=tcube/3 (in m). Find the work done by the force in first 2 seconds

Q. Two springs of spring cons†an t 1500N/m and 3000N/m respectively are stretched with the same force. They will have the potential energy in ratio (1) 4:1 (2) 1:4 (3) 2:1 (4) 1:2

Q. a string is used to pull a block of mass m vertically up by a dis†an ce h at a cons†an t acceleration g/3 The work done by the tension in the tension in the string is

Q. When a mass m is attached to the spring of force cons†an t K, then the spring stretches by l.if the mass oscillates with amplitude l, maximum PE stored in the spring is

Q. a block of 5kg kept on a smooth horizontal surface at rest is acted by an external vertical force F .if the external force displaces the block by 25m where its velocity becomes 8m per sec then work done by external force is

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

Q. Two wires of the young's modulii $Y$ and $2Y$ having lengths $2L,L$ and radii $2R,R$ respectively, are joined end to end as shown in the image. The elastic potential energy stored in the system in equilibrium, is


[Assume the wires are massless and $w$ is the weight hung at the bottom]

1. $\frac{4w^{2}L}{\pi R^{2}Y}$
2. $\frac{w^{2}L}{4\pi R^{2}Y}$
3. $\frac{2w^{2}L}{\pi R^{2}Y}$
4. $\frac{w^{2}L}{2\pi R^{2}Y}$

Q. A long spring is stretched by $2\text{cm}$. Its potential energy is $\text{U}$. If the spring is stretched by $10\text{cm}$, its potential energy would be

1. $\frac{U}{25}$
2. $\frac{U}{5}$
3. $5U$
4. $25U$

Q. A spring of natural length $2x\text{m}$ is elongated such that its extension is twice its original length. If the force constant($k$) of spring is $8\text{N/m}$, the potential energy ($\text{J}$) stored in the spring is:

1. $16x^2$
2. $64x^2$
3. $32x^2$
4. $128x^2$