Which one of the following equations is dimensionally
homogeneous? show your proof.
a. f = ma
b. f = m(v2/r)
c. f(t2 - t1) = m(v2 – v1)
d. f =mv
e. f = m(v2 – v1)/(t2 – t1)
where
f = force (n)
m = mass (kg)
a = acceleration (m/s2)
v = velocity (m/s)
r = radius (m)
t = time (s)

Explanation:

We need to calculate the equations is dimensionally  homogeneous.

We know that,

Unit of force is Newton.

Unit of mass is kg.

Unit of acceleration is m/s².

Unit of velocity is m/s.

Unit of radius is m.

Unit of time is sec.

(a). Given that,

Put the unit of all elements

Here,

This equations is dimensionally  homogeneous.

(b). Given that,

Put the  unit in the formula

This equations is dimensionally  homogeneous.

(c). Given that,

Put the  unit in the formula

This equations is dimensionally  homogeneous.

(d). Given that,

Put the  unit in the formula

This equations is not dimensionally  homogeneous.

(e). Given that,

Put the  unit in the formula

This equations is dimensionally  homogeneous.

Hence, This is required solution.

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