What Is the Variation of Force With Respect to Radius in Circular Orbit?

[Samsmith47]

Homework Statement

The particle is moving in circular orbit such a way that the net force (F) is always towards the point p (point p is on the circumference of circle). Find the variation of force F with respect to r.
i.e find the value of n in the expression F=kr^n

Relevant Equations

F=kr^n
Da/dt= l/2m

Homework Statement: The particle is moving in circular orbit such a way that the net force (F) is always towards the point p (point p is on the circumference of circle). Find the variation of force F with respect to r.
i.e find the value of n in the expression F=kr^n
Homework Equations: F=kr^n
Da/dt= l/2m

Answer is -5
But I am getting -3

 

[haruspex]

Homework Statement: The particle is moving in circular orbit such a way that the net force (F) is always towards the point p (point p is on the circumference of circle). Find the variation of force F with respect to r.
i.e find the value of n in the expression F=kr^n
Homework Equations: F=kr^n
Da/dt= l/2m

Homework Statement: The particle is moving in circular orbit such a way that the net force (F) is always towards the point p (point p is on the circumference of circle). Find the variation of force F with respect to r.
i.e find the value of n in the expression F=kr^n
Homework Equations: F=kr^n
Da/dt= l/2m

Answer is -5
But I am getting -3

Your diagram is too messy to decipher, so I do not know what your variables represent.
Please post a clearer diagram and (as text, not an image) definitions of your variables and consequent working.

 

[sojsail]

Is it possible that your sketch is a misinterpretation of the problem description? If p is on the orbit, when the particle comes around to the location of p, the force would become infinite (with n being a negative exponent). I am assuming that r is the distance to p. And in that case, I can not see why the particle has a circular orbit. Could it be that p is on the circumference of some other circle? Clarify.

 

[haruspex]

when the particle comes around to the location of p, the force would become infinite

Not sure that that is a problem in this artificial scenario.

 

[haruspex]

But I am getting -3

I can see how you would get that if you were to confuse the angular rate of orbit about the centre of the circle with that about P.

 

[Samsmith47]

Thanks for seeing my response I will draw the dia neatly and send again
Sorry for the late reply
And also I got the answer thanks for trying I am really greatfull