If m represents mass in kg, v represents speed in m/s, and r represents radius in m, show that the force f in the equation f=mv^2 /r can be expressed in the unit kg×m/s^2

This approach is called the dimensional analysis which involves only the units of measurement without their magnitudes. You simply have to do the operations by using variables. Cancel out like items that may appear both in the numerator and denominator side. The solution is as follows:

F = mv²/r = [kg][m/s]²/[m] = [kg][m²⁻¹][1/s²] = [kg·m/s²]

The correct answer is c