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If Surface tension (S), Moment of Inert...

If Surface tension (S), Moment of Inertia (I) and Planck’s constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be :

A

`S^(1//2) I^(1//2)h^(0)`

B

`S^(1//2) I^(2//3)h^(-1)`

C

`S^(3//2) I^(1//2)h^(0)`

D

`S^(1//2) I^(1//2)h^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
A
`p-=h^(x)T^(y)I^(z)`
`MLT^(-1)-=(ML^(2) T^(-1))^(x) (MT^(-2))^(y)(ML^(2))^(z)`
`MLT^(-1)=M^(x+y+z).L^(2x+2z)xxT^(-x-2y)`
`{:(x+y+z=1),(x+z=1/2):}}implies y=1/2`
`x +2y =1 implies x +1 =1 implies x =0`
`P = h^(0)S^(1//2)I^(1//2)`
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