Final answer:
The ratio of the accelerations when a solid cylinder rolls down an inclined plane compared to when it slides down is 3:2.
Step-by-step explanation:
The ratio of the accelerations when a solid cylinder rolls down an inclined plane compared to when it slides down is (a) 3:2.
To understand why, we can look at the different types of motion involved. When a solid cylinder rolls down an inclined plane, it undergoes both rotational and translational motion. The net acceleration of the cylinder is the result of the sum of the linear acceleration and the angular acceleration. On the other hand, when the cylinder slides down without rolling, there is only linear acceleration.
Because the ratio of the accelerations is given by the ratio of the linear acceleration to the angular acceleration, we can conclude that the ratio of the accelerations in these conditions is 3:2.
Therefore, option (a) is correct.