Let's break down your question into manageable parts, focusing on each concept step by step. We’ll discuss the binding energy of nuclei, the frequency of revolution in the Bohr model, the collision of masses, and the behavior of charged particles in an electric field. Each section will provide clarity on the principles involved and their implications.

Binding Energy and Fusion of Nuclei

The binding energy per nucleon is a crucial concept in nuclear physics, indicating how much energy is required to remove a nucleon from a nucleus. For the fusion of two hydrogen nuclei (2¹H) to form helium (2⁴He), we can calculate the energy released during this process.

The binding energy per nucleon for 2¹H is approximately 1.1 MeV, while for 2⁴He, it is about 7 MeV. When two hydrogen nuclei fuse, the total binding energy of the resulting helium nucleus is greater than the sum of the binding energies of the individual hydrogen nuclei. The energy released can be calculated as follows:

• Initial binding energy: 2 nuclei × 1.1 MeV = 2.2 MeV
• Final binding energy: 7 MeV (for 2⁴He)
• Energy released: 7 MeV - 2.2 MeV = 4.8 MeV

Thus, the energy released during the fusion of two hydrogen nuclei to form helium is approximately 4.8 MeV, not -2.8 MeV as suggested. The negative sign typically indicates energy absorbed, which is not the case here.

Frequency of Revolution in the Bohr Model

In the Bohr model of the atom, the frequency of revolution of an electron in the nth orbit is given by:

f_n = (1/n²) * f₁

where f₁ is the frequency of the first orbit. This relationship shows that the frequency decreases with the square of the principal quantum number (n). To visualize this, we can plot log(f_n/f₁) against log(n):

Graphical Representation

The graph will show a downward curve, indicating that as n increases, the ratio of frequencies decreases. The relationship is inversely proportional to the square of n, leading to a logarithmic decline:

• X-axis: log(n)
• Y-axis: log(f_n/f₁)

This graph qualitatively represents how the frequency of revolution diminishes as we move to higher energy levels in an atom.

Collision of Masses and Friction

When a ball of mass m falls and collides with a block of equal mass m moving horizontally, we need to consider both the coefficient of restitution and the friction involved. The coefficient of restitution (e) is given as 0.5, which affects how the velocities change post-collision.

Before the collision, the ball has a velocity of v = √(2gh) just before impact. The block has a velocity u. After the collision, we can apply the conservation of momentum and the coefficient of restitution:

• Using conservation of momentum: m(v + u) = m(v₁ + u₁)
• Using the coefficient of restitution: e = (relative speed after)/(relative speed before)

After solving these equations, we find that the velocity of the block decreases by a certain amount, which can be calculated based on the given values. The options provided suggest that the decrease in velocity is related to the height h from which the ball fell.

Acceleration of a Charged Particle

When two identical positive charges are fixed on the Y-axis, they create an electric field that affects a negatively charged particle moving along the X-axis. The acceleration of this particle due to the electric field can be plotted against its position on the X-axis.

As the negatively charged particle approaches the origin (O), it experiences a force due to the electric field created by the positive charges, which results in an acceleration that varies with its distance from the charges:

• Near the origin, the acceleration is strong due to the proximity to the charges.
• As the particle moves further away, the acceleration decreases.

Graphical Representation

The graph of acceleration (a) versus position (x) will show a curve that starts high near the origin and decreases as x increases, illustrating the inverse relationship between distance and electric force.

In summary, each of these concepts illustrates fundamental principles in physics, from nuclear fusion to electric fields and motion dynamics. Understanding these principles helps us grasp the underlying mechanics of various physical phenomena.