First slide

The two types of acceleration

Question

A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to -k/r², where k is a constant. The total energy of the particle is

Moderate

A

$\frac{k}{r}$
B

$\frac{k}{2 r}$
C

$- \frac{k}{2 r}$
D

$\frac{k}{r^{2}}$

Solution

Centripetal force, $F = \frac{{mv}^{2}}{r} = - \frac{k}{r^{2}}$
Negative sign shows that the force is directed towards the centre of the circle.
$\begin{array}{l} ∴ {mv}^{2} = \frac{k}{r} \\ K.E. = \frac{1}{2} {mv}^{2} = k / 2 r \\ P.E. = - k / r \\ ∴ Total energy = \frac{k}{2 r} - \frac{k}{r} = - \frac{k}{2 r} \end{array}$

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