Multiple choice! To be dimensionally consistent, velocity [L/T], force [ML/T^2], mass [M], and length [L] must be related as follows. Multiple Choice A. velocity^2 = force × length/mass B. velocity^2 = force × length/mass^2 C. velocity = force × length^2/mass D. velocity = force × length/mass

velocity^2=force*length/mass

Explanation:

velocity^2=force*length/mass  is dimensionally consistent

as we know that

unit of force=Newton

unit of length=meter

unit of mass=kilogram so

velocity^2=newton*meter/kilogram

newton=kg*m/sec^2 therefore

v^2=kg*m*m/sec^2*kilogram

v^2=kg*m^2/sce^2*kg

v^2=m^2/sec^2

taking square root on both side

√ v²=√m²/sec²

v=m/s  now the dimensions of V is

v=(L/T)

so option A is dimensionally consistent