JEE Advance - Physics (2019 - Paper 1 Offline - No. 12)
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?
The dimension of force is [L]-3
The dimension of power is [L]-5
The dimension of energy is [L]-2
The dimension of linear momentum is [L]-1
Explanation
$$[M] = [Mass] = [{M^0}{L^0}{T^0}]$$
[J] = [Angular momentum] = [ML2T-1]
[L] = [Length]
Now, $$[M{L^2}{T^{ - 1}}] = [{M^0}{L^0}{T^0}]$$
$$ \therefore $$ [L2] = [T]
Power [P] = [MLT2.LT-1] = [ML2T-3]
= [L2L-6]
[P] = [L-4\
Energy/Work [W] = [MLT-2.L]
= [L2L-4] = [L-2]
Force [F] = [MLT-2] = [L.L-4] = [L-3]
Linear momentum [p] = [MLT-1] = [L.L-2]
[p] = [L-1]
[J] = [Angular momentum] = [ML2T-1]
[L] = [Length]
Now, $$[M{L^2}{T^{ - 1}}] = [{M^0}{L^0}{T^0}]$$
$$ \therefore $$ [L2] = [T]
Power [P] = [MLT2.LT-1] = [ML2T-3]
= [L2L-6]
[P] = [L-4\
Energy/Work [W] = [MLT-2.L]
= [L2L-4] = [L-2]
Force [F] = [MLT-2] = [L.L-4] = [L-3]
Linear momentum [p] = [MLT-1] = [L.L-2]
[p] = [L-1]
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