Question

A particle of mass $m$ is executing uniform circular motion on a path of radius $r$. If $v$ is the speed and $p$ the magnitude of its linear momentum, then the radial force acting on the particle is:

• A. $\frac{m{v}^2}{r}$
• B. $\frac{pm}{r}$
• C. $\frac{vp}{r}$
• D. $\frac{p^2}{mr}$

Answer 1

Answer: (A), (C), (D)

The correct options are
A $\frac{m{v}^2}{r}$
C $\frac{vp}{r}$
D $\frac{p^2}{mr}$

Momentum is given as
$p=mv$
the radial force is the centripetal force, so
$F=\frac{m{v}^2}{r}$
also
$F=\frac{(mv{)}^2}{mr}=\frac{p^2}{mr}$
or
$F=\frac{m{v}^2}{R}=\frac{v\left(mv\right)}{r}=\frac{vp}{r}$