Question

as a ball rolls down a ramp, the work done by gravity on the ball is multiple choice positive and independent of the path taken. positive and depends on the path taken. negative and independent of the path taken. negative and depends on the path taken.

Explanation:

Gravity is a conservative force, so work done by it is path - independent. When the ball rolls down the ramp, the displacement in the direction of gravity (vertical) is positive. Work \(W = \vec{F}\cdot\vec{d}=Fd\cos\theta\), here \(F = mg\) (gravity), \(d\) has a component in the direction of \(F\) (so \(\cos\theta> 0\)), so work is positive.

Answer:

A. positive and independent of the path taken.