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Question:

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

The dimension of power isL⁻⁵

The dimension of energy isL⁻²

The dimension of force isL⁻³

The dimension of linear momentum isL⁻¹

Solution:

Correct option is D. The dimension of linear momentum isL⁻¹;
[M]=[Mass]=[M⁰L⁰T⁰]
[J]=[Angular momentum]=[ML²T⁻¹];
[L]=[Length]
Now;
[ML²T⁻¹]=[M⁰L⁰T⁰] ∴[L²]=[T]
Power [P]=[MLT⁻²].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].