Aball rolls without slipping down a tilted plane, starting from rest. at the same time, a box starts from rest and slides down the same plane, although we will assume that there is no friction for the box (note that friction is what allows the ball to roll). which arrives at the bottom first?

Explanation:

This is because the effect that the friction force have depends on the mass, the angle also have a great effect in the answer, but it seems it is not an option, what is worth noticing is that the mass doesn't have effect in the ball rolling given that the friction is only responsible of the rolling.

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The box arrives first.

Explanation:

The ball and the box start from rest and start with the same gravitational potential energy. That potential energy is converted into kinetic energy.

The mass m cancels on both sides of the equation and is not important to the problem.

The difference between the box and the ball comes from rotational energy. Only the ball will gain rotational energy because the box is sliding and will not rotate. The potential energy of the ball will be converted into kinetic and rotational energy. This means the kinetic energy of the ball will be smaller than the kinetic energy of the box, hence the box will be faster.

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