By Team Aakash Byju's | 7th December 2022
A
In a system of units where the mass and angular momentum are dimensionless, and length has a dimension of L, then
The dimension of force is L
-3
B
The dimension of power is L
-5
C
D
The dimension of energy is L
-2
The dimension of linear momentum is L
-1
The correct options are
-1
-3
A. The dimension of force is L
C. The dimension of energy is L
D. The dimension of linear momentum is L
-2
We know that angular momentum can be written as
J = mvr
where, m is the mass whose dimension is M v is the velocity whose dimension is L T r is the distance whose dimension is L
1
1
-1
1
Thus, angular momentum in terms of dimension is
J = [M L T L ] = [M L T ]
M = [M L T ]
1
-1
1
=> L T = 1 => L = T
(Because mass and angular momentum are dimensionless)
1
1
2
-1
1
1
2
-1
2
-1
2
1
The dimensions of Linear momentum are
=> P = [M][LT ] = [M L T ]
=> P = [L L ]
(because mass is dimensionless and T = L or T = L )
2
1
-1
=> P = L (Option D)
1
1
-1
1
-2
-1
-2
-1
The dimensions for force when the mass is dimensionless can be written as,
Force = [L T ] and since T = L => T = L
=>Force = [L L ] = L (Option A)
1
-4
1
2
-2
1
-2
-4
-3
In terms of dimension formula, both Energy and Work done are the same.
Energy = Work = Force x displacement
=> Energy = [L T ] [L] = [L T ]
2
1
-2
-2
=> Energy = [L L ] = [L ] (Option C)
2
-4
-2
1
Since L = T
2
=> T = L
-2
-4
=> P = [MLT ] [LT ] =[M L T ]
-1
-2
Now, let us check the correctness of option B. We know that, Power = Force x velocity
2
-3
2
=> P = [L ] that is why Option B is incorrect.
=> P = [L L ] (Because mass is dimensionless and T = L => T = L )
1
-4
-3
-6
2
2
-6