Two springs \(\mathrm{A}\) and \(\mathrm{B}\) \((k_A=2k_B)\) are stretched by applying forces of equal magnitudes at the four ends. If the energy stored in \(\mathrm{A}\) is \(E,\) that in \(\mathrm{B}\) is:
1. \(\frac{E}{2}\)

2. \(2E\)    

3. \(E\)

4. \(\frac{E}{4}\)

Two equal masses are attached to the two ends of a spring of spring constant k. The masses are pulled out symmetrically to stretch the spring by a length x over its natural length. The work done by the spring on each mass is

1. \(\frac{1}{2} \mathrm{kx}^{2}\)

2. \(-\frac{1}{2} \mathrm{kx}^{2}\)

3. \(\frac{1}{4} \mathrm{kx}^{2}\)

4. \(-\frac{1}{4} \mathrm{kx}^{2}\)

The negative of the work done by the conservative internal forces on a system equals the change in:
1. total energy
2. kinetic energy
3. potential energy
4. none of these

One end of a light spring of spring constant k is fixed to a wall and the other end is tied to a block placed on a smooth horizontal surface. In a displacement, the work done by the spring is \(\frac{1}{2}\)kx². The possible causes are

(a) the spring was initially compressed by a distance and was finally in its natural length

(b) it was initially stretched by a distance of x and was in its natural length

(b) it was initially in its natural length and finally in the compressed position

(d) it was initially in its natural length and finally in a stretched position

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. All of these