Given:
Mass of the rope (m) = 0.1 kg
Length of the rope (L) = 2.45 m
Acceleration due to gravity (g) = 9.8 m/s^2

To Find:
Time taken by a transverse wave to travel the full length of the rope

Explanation:
A transverse wave is a type of wave in which the particles of the medium vibrate perpendicular to the direction of wave propagation. In the case of a rope, the wave travels along the length of the rope while the particles of the rope move up and down perpendicular to the direction of the wave.

The velocity of a wave on a rope can be calculated using the formula:
v = √(T/μ)
where v is the velocity of the wave, T is the tension in the rope, and μ is the linear mass density of the rope.

Calculating Tension in the Rope:
The tension in the rope is equal to the weight of the rope, which can be calculated using the formula:
T = mg
where m is the mass of the rope and g is the acceleration due to gravity.

T = 0.1 kg × 9.8 m/s^2 = 0.98 N

Calculating Linear Mass Density:
The linear mass density of the rope can be calculated using the formula:
μ = m/L
where m is the mass of the rope and L is the length of the rope.

μ = 0.1 kg / 2.45 m = 0.0408 kg/m

Calculating Velocity of the Wave:
Using the values of tension (T) and linear mass density (μ), we can calculate the velocity (v) of the wave.
v = √(T/μ) = √(0.98 N / 0.0408 kg/m) = √(24.02 m^2/s^2) = 4.901 m/s

Calculating Time Taken:
The time taken by a wave to travel a distance is given by the formula:
time = distance / velocity

In this case, the distance is equal to the length of the rope (L), and the velocity is 4.901 m/s.
time = 2.45 m / 4.901 m/s = 0.5 s

However, we need to consider that the wave travels the full length of the rope and returns back to its starting position. Therefore, the total time taken will be twice the time calculated above.
total time = 2 × 0.5 s = 1 s

Hence, the correct answer is 1 second.