To calculate the ratio of the equivalent moment to equivalent torque, we need to first understand the concept of equivalent moment and equivalent torque in a cantilever beam.

A cantilever beam is a type of beam that is fixed at one end and free at the other end. When a cantilever beam is subjected to external loads, it experiences both bending moment and twisting moment.

Bending moment is a measure of the internal forces in a beam that cause it to bend. It is calculated by multiplying the applied force by the distance from the point of application to the fixed end of the beam. In this case, the bending moment is given as 8kNm.

Twisting moment, also known as torque, is a measure of the internal forces in a beam that cause it to twist. It is calculated by multiplying the applied force by the distance from the point of application to the fixed end of the beam. In this case, the twisting moment is given as 12kNm.

Now, let's calculate the equivalent moment and equivalent torque.

The equivalent moment is the moment that would produce the same effect as the combined bending moment and twisting moment on the cantilever beam. It is calculated by taking the square root of the sum of the squares of the bending moment and twisting moment.

Equivalent moment = √(bending moment^2 + twisting moment^2)
= √((8kNm)^2 + (12kNm)^2)
= √(64kNm^2 + 144kNm^2)
= √(208kNm^2)
≈ 14.42kNm

The equivalent torque is the torque that would produce the same effect as the combined bending moment and twisting moment on the cantilever beam. It is calculated by taking the maximum value of the bending moment or twisting moment.

Equivalent torque = max(bending moment, twisting moment)
= max(8kNm, 12kNm)
= 12kNm

Now, we can calculate the ratio of the equivalent moment to equivalent torque.

Ratio = equivalent moment / equivalent torque
= 14.42kNm / 12kNm
≈ 1.20

Therefore, the ratio of the equivalent moment to equivalent torque is approximately 1.20.

The correct answer is option B) 2.

The given options are:
a) 1
b) 2
c) 0.77
d) 0.5

None of the options match the calculated ratio of 1.20.