A particle of mass M moves with constant speed along a circular path of radius r under the action of a force F. Its speed is

The correct option is √(rF/m).

To find the speed of the particle, we can analyze the forces acting on it during circular motion. When a particle of mass $m$ moves along a circular path of radius $r$ with a constant speed $v$, it experiences a centripetal acceleration directed towards the center of the circle.

The centripetal force $F$ required to maintain this circular motion is given by the formula:
$F=\frac{m{v}^2}{r}$

To solve for the speed $v$, we rearrange the equation step-by-step:

First, multiply both sides of the equation by the radius $r$:
$F·r=m{v}^2$

Next, divide both sides by the mass $m$ to isolate $v^2$:
$v^2=\frac{Fr}{m}$

Finally, take the square root of both sides to find the speed $v$:
$v=\sqrt{\frac{rF}{m}}$

This matches the expression √(rF/m).