Question

A solid sphere of radius r is placed on an incline that makes an angle θ with the horizontal. The sphere rolls down the incline without slipping. Which of the following statements is correct regarding this scenario?

a) The sphere experiences both translational and rotational kinetic energy.
b) The sphere only experiences translational kinetic energy.
c) The sphere only experiences rotational kinetic energy.
d) The sphere experiences potential energy but no kinetic energy.

Answer 1

The solid sphere rolling down an incline without slipping experiences both translational and rotational kinetic energy, reflecting the correct option as a) in the provided choices.

Step-by-step explanation:

When a solid sphere is placed on an incline and rolls down without slipping, it experiences both translational kinetic energy and rotational kinetic energy. This is because as the sphere rolls down, it not only moves down the incline (translation) but also spins around its axis (rotation). The correct answer to the student's question is a) The sphere experiences both translational and rotational kinetic energy. If the sphere were simply sliding down the incline without rolling, all its potential energy would convert into translational kinetic energy only. However, because it rolls, the potential energy is split between translational and rotational kinetic energy, meaning it descends at a rate slower than it would if it were sliding without friction.