Question 113: Work, Energy and Power & Circular Motion

Question

A particle of mass m moves in a circular orbit under the central potential field, $$U(r) =  - {C \over r}$$, where C is a positive constant. The correct radius $$-$$ velocity graph of the particle's motion is :

Accepted Answer

Given potential field U(r) = $${{ - C} \over r}$$
$$ \because $$ $$F = {{dU} \over {dr}} = {C \over {{r^2}}}$$
& $${F_c} = {{m{v^2}} \over r}$$
$$ 	herefore $$ $${{m{v^2}} \over r} = {C \over {{r^2}}}$$
$$ \Rightarrow r = {C \over {m{v^2}}}$$
$$ \Rightarrow r$$ $$ \propto $$ $$ {1 \over {{v^2}}}$$
$$ 	herefore $$ the graph between r & v will be hyperbolic.

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Work, Energy and Power & Circular Motion

A particle of mass m moves in a circular orbit under the central potential field, $U(r) = - {C \over r}, where C is a positive constant. The correct radius -$ velocity graph of the particle's motion is :

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