To solve this problem we will use the concepts of the moment of rotational inertia, angular acceleration and the expression of angular velocity.
The rotational inertia is expressed as follows:
Here,
m = Mass of the object
r = Distance from the rotational axis
The rotational acceleration in terms of translational acceleration is
Here,
a = Acceleration
R = Radius of the circular path of the object
The expression for the rotational speed of the object is
Here,
is the angular displacement of the object
The explanation by which when climbing a mountain uphill is changed to a larger pinion, is because it produces a greater torque but it is necessary to make more pedaling to be able to travel the same distance. Basically every turn results in less rotations of the rear wheel. Said energy that was previously used to move the rotation of the wheel is now distributed in more turns of the pedal. Therefore option a and c are correct.
This would indicate that the correct option is D.