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Question

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?

A
The dimension of force is L3
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B
The dimension of power is L5
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C
The dimension of linear momentum is L1
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D
The dimension of energy is L2
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Solution

The correct options are
A The dimension of force is L3
C The dimension of linear momentum is L1
D The dimension of energy is L2
Angular momentum ()=mvr[]=ML2TMdimensionless

T=L2 also dimensionless
Now p=mv=MLT
[p]=L1

[ Energy ]=ML2T2=L2L2L2=L2

[Power ]=ML2T2T=L2L2L2L2=L4

[Force] =MLT2=LL2L2=L3

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