Binding Energy and Fission
The binding energy of a nucleus is the energy required to completely separate its nucleons (protons and neutrons) from each other. It is a measure of the stability of the nucleus. The binding energy per nucleon is the total binding energy divided by the number of nucleons in the nucleus. In this case, we are given that the binding energy per nucleon for a heavy nucleus is 7 MeV and for a medium weight nucleus is 8 MeV.

Fission Reaction
Fission is a nuclear reaction in which a heavy nucleus splits into two lighter nuclei, accompanied by the release of a large amount of energy. In symmetric fission, the two resulting nuclei have approximately the same mass. The total kinetic energy liberated in this process can be calculated using the conservation of energy.

Calculation
Let's assume the heavy nucleus has a mass number A. During symmetric fission, it splits into two nuclei, each with a mass number of A/2. The total binding energy of the heavy nucleus is then 7 MeV/nucleon * A, and the total binding energy of the two resulting nuclei is 8 MeV/nucleon * (A/2).

The conservation of energy tells us that the total energy before fission is equal to the total energy after fission. The total energy before fission is the sum of the kinetic energy of the heavy nucleus (K1) and its binding energy (B1). The total energy after fission is the sum of the kinetic energy of the two resulting nuclei (K2 and K3) and their binding energies (B2 and B3).

K1 + B1 = K2 + K3 + B2 + B3

Since the resulting nuclei have the same mass, their kinetic energies are equal (K2 = K3 = K). Substituting the binding energies, we have:

K1 + B1 = 2K + 2B2

We know that the binding energy per nucleon for the heavy nucleus is 7 MeV, so B1 = 7 MeV * A. We also know that the binding energy per nucleon for the resulting nuclei is 8 MeV, so B2 = 8 MeV * (A/2). Substituting these values, we have:

K1 + 7 MeV * A = 2K + 2 * 8 MeV * (A/2)

Simplifying the equation, we get:

K1 + 7 MeV * A = 2K + 8 MeV * A

Rearranging the equation, we find:

K1 - 2K = 8 MeV * A - 7 MeV * A

K1 - 2K = MeV * A

This equation tells us that the kinetic energy liberated during symmetric fission is equal to the difference between the initial kinetic energy of the heavy nucleus and twice the kinetic energy of one of the resulting nuclei. Since we are asked to find the total kinetic energy liberated, we need to find the value of K1 - 2K.

Answer
The correct answer is 200 MeV.