B

The formula for centripetal force, which is responsible for keeping an object moving in a circular path, is given by:
F_c = \frac{mv^2}{r}
where F_c is the centripetal force, m is the mass of the object, v is the speed of the object, and r is the radius of the circular path.

Now, let's analyze the given options:
Option A: mv - Incorrect; this represents momentum.
Option B: \frac{mv^2}{r} - Correct; this matches our derived formula for centripetal force.
Option C: \frac{v}{r}m - Incorrect; this doesn't represent centripetal force correctly.
Option D: \frac{v}{r}m - Again, incorrect for the same reasons as C.

Therefore, the correct answer is B.