Let us consider a system of units in which mass and angular momentum are dimensionless. If length has…

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?
  1. The dimension of power is L-5
  2. The dimension of force is L-3
  3. The dimension of linear momentum is L-1
  4. The dimension of energy is L-2 '

Solution

M=Mass=M0L0T0
J=Angular momentum=ML2T-1
L=Length
[Now as angular momentum is dimensionless]
ML2T-1=M0L0T0
∴L2=T
∴ Power P=MLT-2⋅LT-1 as P=F⋅V
=ML2T-3
=L2L-6
⇒[P]=[L-4]⇒(A) is incorrect.
Energy/Work W=MLT-2⋅L (using, Work=Force×displacement
=L2L-4
=L-2⇒D is correct.
Force F=MLT-2=L⋅L-4=L-3⇒(B) is correct.
Linear momentum P=MLT-1=L⋅L-2
p=L-1⇒C is correct.

Asked in: JEE Advanced 2019 (Paper 1)

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