Question

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in which one of the following circumstances does the principle of conservation of mechanical energy apply, even though a nonconservative force acts on the moving object?
the nonconservative force has a component that points in the same direction as the displacement of the object.
the nonconservative force is perpendicular to the displacement of the object.
the nonconservative force has a component that points opposite to the displacement of the object.
the nonconservative force has a direction that is opposite to the displacement of the object.
the nonconservative force points in the same direction as the displacement of the object.

Explanation:

The principle of conservation of mechanical energy applies when non - conservative forces do no work. Work done by a force is given by $W = \vec{F}\cdot\vec{d}=Fd\cos\theta$, where $\theta$ is the angle between the force $\vec{F}$ and displacement $\vec{d}$. When the non - conservative force is perpendicular to the displacement ($\theta = 90^{\circ}$), $\cos\theta=0$ and the work done by the non - conservative force is zero. So mechanical energy is conserved.

Answer:

The nonconservative force is perpendicular to the displacement of the object.