Let us consider a system of units in which mass and angular momentum are dimensionless. If the length has a dimension of L, which of the following statement(s) is/are correct?
The dimension of force is
The dimension of power is
The dimension of linear momentum is
The dimension of energy is
The dimension of energy is
The explanation for the correct options:
In the case of options A, C, and D.
Step 1. Explanation:
We know
Now;
Since mass is dimensionless, therefore now we are left with
Comparing LHS with RHS, we get
∴
Step 2. Dimensions:
Finding dimensions of Energy:
Energy =
=mass, =velocity
Velocity=
Therefore, Energy/work
=
=
Finding dimensions of Force:
Force = Mass × Acceleration
Since, acceleration = velocity / time =
Force
Finding dimensions of Linear momentum :
Linear Momentum = Mass × Velocity
Mass =, Velocity =
So Linear momentum
Hence, the correct options are options A, C, and D.
The explanation for the incorrect option:
In the case of option B.
Finding dimensions of Power:
Writing the dimensional formula of all the above values, we get
Power
=
=
Hence, option B is the incorrect option.
Hence, the correct options are options A, C, and D.