JEE Main 2016 · 10 Apr · Shift 1 · Physics Q1

← JEE Main 2016 · 10 Apr · Shift 1

PhysicsSingle correct+4 / -1Question 1 of 90

A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD = C ln(BD) holds true. Then which of the combination is not a meaningful quantity ?

A^2-B^2C^2

\dfrac{(A-C)}D

\dfrac AB-C

\dfrac C{BD}-\dfrac{AD^2}C

Answer and worked solution

Official answer: B

The argument of ln must be dimensionless, so $[B]=[D]^{-1}$ , and then $[C]=[AD]$ .

(1): $[BC]=[A]$ , so $A^2-B^2C^2$ is meaningful.
(2): A and C have different dimensions, so $A-C$ is not meaningful.
(3): $\frac AB=[AD]=[C]$ , meaningful.
(4): $\frac C{BD}$ has the dimensions of C, while $\frac{AD^2}C=[D]$ ; these differ, so (4) is not meaningful either.

The intended answer is (2); since (4) also fails, this derived key accepts both.

Topics:Dimensional analysis

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JEE Main 2016 · 10 Apr · Shift 1, Physics question 1