Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimensions of L, which of the following statement(s) is/are correct? [2019]

Question

Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimensions of L, which of the following statement(s) is/are correct? [2019]

Smart Achievers · Accepted Answer

(1, 2, 3)

$According to question, dimensions of angular momentum [m v r] = M^{0} L^{0} T^{0} and of mass [m] = M^{0} L^{0} T^{0}$

$M L^{2} T^{- 1} = M L^{0} T^{0} \Rightarrow T = L^{2}$

Momentum $p = m v = \frac{m v r}{r} = \frac{M^{0} L^{0} T^{0}}{L} = \frac{L}{L^{2}} = L^{- 1}$

Energy $E = \frac{1}{2} m v^{2} = \frac{1}{2} \frac{{(m v)}^{2}}{m} = L^{- 2}$

Power $P = \frac{E}{t} = \frac{L^{- 2}}{T} = \frac{L^{- 2}}{L^{2}} = L^{- 4}$

Force $F = \frac{E}{x} = \frac{L^{- 2}}{L} = L^{- 3}$

Solution

Q.
Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimensions of L, which of the following statement(s) is/are correct [2019]

1 The dimension of force is $L^{- 2}$

2 The dimension of linear momentum is $L^{- 1}$

3 The dimension of energy is $L^{- 2}$

4 The dimension of power is $L^{- 5}$

Want Us to Email you About Special Offers & Updates?

Solution

Q. Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimensions of L, which of the following statement(s) is/are correct [2019]

1 The dimension of force is L-2

2 The dimension of linear momentum is L-1

3 The dimension of energy is L-2

4 The dimension of power is L-5