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Which of the following is dimensionless?...

Which of the following is dimensionless?

A

`(v^(2))/(rg)`

B

`(v^(2)g)/r`

C

`(vg)/r`

D

`(v^(2))rg`

Text Solution

Verified by Experts

The correct Answer is:
A
(i) `(v^(2))/(rg)=([LT^(-1)]^(2))/([L][LT^(-2)])," "(v^(2))/(rg)` is dimensionless
(ii) `(v^(2)g)/r=([LT^(-1)]^(2)[LT^(-2)])/([L])=L^(2)T^(-4)`
(iii) `(vg)/r=([LT^(-1)][LT^(-2)])/([L])=LT^(-3)`
(iv) `v^(2)rg=[LT^(-1)][L][LT^(-2)]=[L^(4)T^(-4)]`
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