Question 154: Units , Dimensions and Error Analysis

Question

If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units. Then the dimension of mass (m) in terms of t, v and l is :

Accepted Answer

$$m \propto {t^a}{v^b}{l^c}$$
$$m \propto {[T]^a}{[L{T^{ - 1}}]^b}{[M{L^2}{T^{ - 1}}]^c}$$
$${M^1}{L^0}{T^0} = {M^c}{L^{b + 2c}}{T^{a - b - c}}$$
comparing powers
c = 1, b = $$-$$2, a = $$-$$1
$$m \propto {t^{ - 1}}{v^{ - 2}}{l^1}$$

Answer

$$[{t^{ - 1}}{v^1}{l^{ - 2}}]$$

Answer

$$[{t^1}{v^2}{l^{ - 1}}]$$

Answer

$$[{t^{ - 2}}{v^{ - 1}}{l^1}]$$

Answer

$$[{t^{ - 1}}{v^{ - 2}}{l^1}]$$

Units , Dimensions and Error Analysis

If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units. Then the dimension of mass (m) in terms of t, v and l is :

Choose the correct answer: