If `A=B+ (C)/(D+E)` the dimensions of B and Care `[M^(0)LT^(-1)]` and `[M^(0)LT^(0)]`, respectively. Find the dimensions of A, D and E.

Options

A. `[A]= [M^(0)L^(0)T^(-1)], [D]= [T], [E]= [LT]`
B. `[A]= [MLT^(0)], [D]= [T^(2)], [E]= [T^(2)]`
C. `[A]= [M^(0)LT^(-1)], [D]= [MT], [E]= [MT]`
D. `[A]= [M^(0)LT^(-1)], [D]= [T], [E]= [T]`

Answer

D

Explanation

As `A= B+ (C)/(D+E)`
`:. [D]= [E]`
`:. [A]= [B]= [(C)/(D+E)]= [(C)/(D)]= [(C)/(E)] :. [A]= [B]= [M^(0)LT^(-1)]`

`[(C)/(D)]= [A]= [M^(0)LT^(-1) ]`
`[D]= [E]= [(C)/(LT^(-1)] = ( [M^(0)LT^(0) ])/( [M^(0)LT^(-1) ])= [T]`