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Question

Time (T), Velocity (C), and angular momentum (h) is chosen as fundamental quantities instead of mass, length, and time. In terms of these, the dimension of mass would be


A

[M]=[T-1C-2h]

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B

[M]=[T-1C2h]

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C

[M]=[T-1C-2h-1]

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D

[M]=[TC-2h]

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Solution

The correct option is A

[M]=[T-1C-2h]


Step 1: Given Data

The fundamental quantity of time =T

The fundamental quantity of velocity =C

The fundamental quantity of angular momentum =h

Step 2: Formula Used

The dimension of mass can be given as,

MTxCyhz

Step 3: Dimension of Mass

The dimension of mass can be given as,

MTxCyhz

We know that the dimension of mass is,

[M1L0T0]=TxCyhz=[Tx][LT-1]y[ML2T-1]z=MzLy+2zTx-y-z

On comparing the powers, we get,

z=1.(1)

y+2z=0y+2=0y=-2.(2)

x-y-z=0x+2-1=0x=-1.(3)

Therefore, upon substituting we get,

[M]=[T-1C-2h]

Hence, the correct answer is option (A).


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