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If momentum (p), area (A) and time(t) ar...

If momentum `(p)`, area `(A)` and time`(t) `are taken to be fundamental quantities then energy has the dimensional formula

A

`[pA^(-1) T^(1)]`

B

`[p^(2) AT]`

C

`pA^(-1//2)T]`

D

`[pA^(1//2) T]`

Text Solution

Verified by Experts

The correct Answer is:
D
`E prop p^(a) A^(b) T^(c)`
`E = kp^(a) A^(A) T^(C)`
`ML^(2) T^(-2) - [MLT^(-1)]^(a) [L^(2)]^(b) [T]^(c)`
`= M^(a) L^(2b+a) T^(a+c)`
On solving `E = pA^(1//2) T^(-1)`.
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