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

Question

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

Tardigrade Admin · Accepted Answer

U =-( C / r ) F =-( d U / dr )=-( C / r 2) | F |=( mv 2/ r ) ( C / r 2)=( mv 2/ r ) v 2 propto (1/ r )

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

$U = - \frac{C}{r}$
$F = - \frac{d U}{d r} = - \frac{C}{r ^{2}}$
$∣ F ∣ = \frac{m v ^{2}}{r}$
$\frac{C}{r ^{2}} = \frac{m v ^{2}}{r}$
$v^{2} \propto \frac{1}{r}$

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

U=−rC​ F=−drdU​=−r2C​ ∣F∣=rmv2​ r2C​=rmv2​ v2∝r1​

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

$U = - \frac{C}{r}$
$F = - \frac{d U}{d r} = - \frac{C}{r ^{2}}$
$∣ F ∣ = \frac{m v ^{2}}{r}$
$\frac{C}{r ^{2}} = \frac{m v ^{2}}{r}$
$v^{2} \propto \frac{1}{r}$