Question

Q 2. Object is moving on a circular path under the action of conservative force F = - k/r². Then find kinetic energy, potential energy and mechanical energy. [IIT]

Answer 1

Answer:

The kinetic , potential and mechanical energy of the body is $\frac{1}{2} mv^2$, $\frac{-2k}{r^3}$ and$\frac{1}{2} mv^2-\frac{2k}{r^3}$ respectively.

Explanation:

The force acting on the object on a circular path is given by F =  $\frac{-k}{r^2}$,

• Kinetic energy of a body moving in a circular path depends only on the velocity. Hence the kinetic energy is given as T = $\frac{1}{2} mv^2$

• Potential energy is defined as V=$-\int {F.} \, dr$

$\int{\frac{k}{r^2} } \, dr =-2\frac{k}{r^3}$ , Hence Potential energy = $\frac{-2k}{r^3}$.

• Mechanical energy (E) is defined as sum of potential and kinetic energy hence, E = T+V=  $\frac{1}{2} mv^2$+$\frac{-2k}{r^3}$