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

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23-08-2020
Physics

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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

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kk5996282 kk5996282 · Answer 1 · 2020-08-23T19:48:31+02:00

Answer:

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

andromache andromache · Answer 2 · 2022-03-18T06:26:51+01:00

It should be related like velocity^2=force*length/mass

Calculation of the relationship:

Since we know that

unit of force=Newton

unit of length=meter

And,

unit of mass=kilogram

Therefore,

velocity^2=newton*meter/kilogram

Now

newton=kg*m/sec^2

So,

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

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

v^2=m^2/sec^2

Now we take square root on both side

So,

√ v²=√m²/sec²

v=m/s

v=(L/T)

Therefore, option A is correct

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