If in a hypothetical system if the angular momentum and mass are dimensionless. Then which of the following is true.

Options

A. The linear momentum varies as `L^(-1)`
B. The energy varies as `L^(-2)`
C. The power varies as `L^(-4)`
D. The force varies as `L^(-5)`

Answer

A, B, C

Explanation

[M]=[Mass]=`[M^(0)L^(0)T^(0)]`
[J] =[Angular momentum] =`[ML^(2)T^(-1)]`
Now, `[ML^(2)T^(-1)]=[M^(0)L^(0)T^(0)]`
`:.[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]`
Force [F] `=[MLT^(-2)]=[L.L^(-4)]=[L^(-3)]`
Linear momentum [p]=`[MLT^(-1)]=[L.L^(-2)]`
`[p]=[L^(-1)]`