The types of motion which a cylindrical drum rolling down an inclined plane undergoes are

Analyze the question: A cylindrical drum rolls down an inclined plane. We need the types of motion involved.

Concept:

• Translational motion: the whole body moves from one place to another. The drum's centre of mass moves down the slope in a straight line.
• Rotational motion: the body spins about its own axis. The drum turns about its central axis as it rolls.
• Circular motion is movement along a circular path around an external point. The drum is not travelling in a circle, so this does not apply.
• Rectilinear motion is straight-line motion. It is really a form of translation, but it is not paired with a correct second motion in the options.

Solution:

1. The drum's centre moves down the incline, so it has translational motion.
2. At the same time, the drum spins about its axis, so it has rotational motion.
3. Rolling without slipping combines these two: v = ωr.
4. Check the options: • A: circular and translational. Circular is not correct here. • B: rotational and translational. Both are correct. • C: rotational and circular. Translation is missing. • D: rectilinear and circular. Circular is wrong, and rotation is missing.

Answer: B. rotational and translational

Tip: Think of "rolling = spinning + travelling". Any rolling object, such as a wheel, ball or drum, combines rotation about its axis with translation of its centre. A similar question can ask about a ball rolling on the ground, and the answer follows the same reasoning.