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If speed (V),acceleration (A) and force...

If speed (V),acceleration (A) and force (F) are considered as fundamental units, the dimesnion of Young 's modulus will be :

A

`V^(-4)A^(2)F`

B

`V^(-2)A^(2)F^(-2)`

C

`V^(-2)A^(2)F^(2)`

D

`V^(-4)A^(-2)F`

Text Solution

Verified by Experts

The correct Answer is:
A
`[y]=[V_(X)A^(Y)F^(Z)]`
or `[mL^(-1)T^(-2)]=(LT^(-1))^(X)(LT^(-2))^(Y)(mLT^(-2))^(z)]or(mL^(-1)T^(-2)]=(m^(Z)L^(X+Y+Z)T^(-X-2Y-2Z))`
Comparing powers of m, L and T on both sides.
`z=1`
`X+Y+Z=-1`
`-x-2Y-2z=-2rArrx=-4`
`y=2`
`z=1therefore` Required dimensional formula is `V^(-4)A^(2)F`.
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