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Using force, length, and time as fundamental quantities, what are the dimensions of mass?

Using force, length, and time as fundamental quantities, what are the dimensions of mass?

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
8 years ago
Newton’s second law of motion states that, force acting on an object (F) from rest is equal to the mass of the object (m) times the acceleration of the object (a).
So, F = ma …… (1)
Rearranging the above equation, mass of the object (m) will be
m = F/a …… (2)
Acceleration of a body (a) is the rate of change of velocity (v) and velocity is the rate of change displacement (s).
So, a = v/t
= (s/t)/t
= s/t2 …… (3)
Since length and time as fundamental quantities, so the dimensions of acceleration will be
[a] = [s/t2 ]
= LT -2 …… (4)
Using equation (2) and force, length, and time as fundamental quantities, the dimensions of mass would be,
[m] = [F/a ]
= F/ LT -2
= FL-1T2 …… (5)
From equation (5), we observe that, using force, length, and time as fundamental quantities, the dimension of mass would be FL-1T2.

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