**Explanation:**

When a cricket ball is hit at an angle of 45 degrees to the horizontal with a velocity v, it follows a parabolic trajectory. At the topmost point of its trajectory, the ball momentarily comes to rest before starting to fall back downwards.

To find the kinetic energy at the topmost point, we need to consider the conservation of mechanical energy. At the topmost point, the ball has only potential energy and no kinetic energy. This means that the initial kinetic energy of the ball is converted entirely into potential energy at that point.

**1. Conservation of Mechanical Energy:**

The conservation of mechanical energy states that the total mechanical energy of a system remains constant if no external forces are acting on it. In this case, we can assume that there are no external forces acting on the cricket ball (such as air resistance), so we can apply the conservation of mechanical energy.

**2. Initial Kinetic Energy:**

The initial kinetic energy of the cricket ball can be calculated using the formula:

Kinetic Energy = (1/2) * mass * velocity^2

Therefore, the initial kinetic energy of the ball is given by:

Initial Kinetic Energy = (1/2) * m * v^2

**3. Final Potential Energy:**

At the topmost point of the ball's trajectory, the potential energy is given by:

Potential Energy = mass * gravity * height

Since the ball reaches its maximum height at the topmost point, the height can be calculated using the vertical component of the initial velocity:

height = (velocity^2 * sin^2(angle)) / (2 * gravity)

Substituting this value into the potential energy equation, we get:

Potential Energy = m * gravity * [(velocity^2 * sin^2(angle)) / (2 * gravity)]

Potential Energy = (1/2) * m * velocity^2 * sin^2(angle)

**4. Final Kinetic Energy:**

Since the ball comes to rest at the topmost point, its final kinetic energy is zero.

**5. Conclusion:**

From the conservation of mechanical energy, we know that the initial kinetic energy is equal to the final potential energy plus the final kinetic energy.

Initial Kinetic Energy = Final Potential Energy + Final Kinetic Energy

(1/2) * m * v^2 = (1/2) * m * velocity^2 * sin^2(angle) + 0

Therefore, the kinetic energy at the topmost point is given by:

Kinetic Energy = (1/2) * m * v^2 * sin^2(angle)

In this case, the angle is 45 degrees, so sin^2(45) = 1/2.

Therefore, the kinetic energy at the topmost point is:

Kinetic Energy = (1/2) * m * v^2 * (1/2)

Kinetic Energy = mv^2/4

Hence, the correct option is 3. mv^2/4.