Calculate the amount of work done in moving a body in one complete rotation about a circle of radius 7m in which force of 10N is applied.

Question

Accepted Answer

The correct option is (2):

When a body moves in a complete circular rotation, and the force applied is a centripetal force (acting towards the center of the circle), the work done by this force is zero. This is because work done ($W$) is defined as the dot product of the force vector ($\vec{F}$) and the displacement vector ($\vec{d}$), which can be written as $W = Fd \cos{	heta}$, where $	heta$ is the angle between the force and the displacement. In uniform circular motion, the centripetal force is always directed towards the center of the circle, while the instantaneous displacement of the body is always tangential to the circle. Therefore, the angle $	heta$ between the centripetal force and the displacement is always $90^\circ$. Since $\cos(90^\circ) = 0$, the work done by the centripetal force over any displacement, and thus over a complete rotation, is zero. Even though a force of $10	ext{ N}$ is applied and the body moves a distance equal to the circumference of the circle ($2\pi r$), the work done by this force (assuming it's the centripetal force) is zero because its direction is always perpendicular to the direction of motion.

The incorrect option is (1): $440	ext{ J}$
This option might be obtained by incorrectly calculating work as force multiplied by the circumference ($W = F 	imes 2\pi r$), without considering the angle between the force and displacement.

The incorrect option is (3): $220	ext{ J}$
This option also results from an incorrect application of the work formula, likely involving some partial calculation or an erroneous value for the distance or angle.

The incorrect option is (4): $22	ext{ J}$
This option is also incorrect and likely stems from a misunderstanding of the work-energy theorem or the definition of work in circular motion, leading to a significantly underestimated value.