Question 290: Units , Dimensions and Error Analysis

Question

Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of L, which of the following statement(s) is/are correct?

Accepted Answer

$$[M] = [Mass] = [{M^0}{L^0}{T^0}]$$
[J] = [Angular momentum] = [ML
2
T
-1
]
[L] = [Length]
Now, $$[M{L^2}{T^{ - 1}}] = [{M^0}{L^0}{T^0}]$$
$$ 	herefore $$ [L
2
] = [T]
Power [P] = [MLT
2
.LT
-1
] = [ML
2
T
-3
]
= [L
2
L
-6
]
[P] = [L
-4
\
Energy/Work [W] = [MLT
-2
.L]
= [L
2
L
-4
] = [L
-2
]
Force [F] = [MLT
-2
] = [L.L
-4
] = [L
-3
]
Linear momentum [p] = [MLT
-1
] = [L.L
-2
]
[p] = [L
-1
]

Answer

The dimension of force is [L]
-3

Answer

The dimension of power is [L]
-5

Answer

The dimension of energy is [L]
-2

Answer

The dimension of linear momentum is [L]
-1

Units , Dimensions and Error Analysis

Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of L, which of the following statement(s) is/are correct?

Choose the correct answer: