JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Units & Measurement

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

Answer: (D)

Solution

Young's modulus is a stress,

[Y] = [M L^{- 1} T^{- 2}]

, and the task is to rebuild

M

L

and

T

from speed

V

, acceleration

A

and force

F

. From

F = M A

[M] = [F A^{- 1}]

; from

A = V / T

[T] = [V A^{- 1}]

, and then

[L] = [V T] = [V^{2} A^{- 1}]

. Substituting,

[Y] = [F A^{- 1}] [V^{2} A^{- 1}]^{- 1} [V A^{- 1}]^{- 2} = [F A^{- 1}] [V^{- 2} A] [V^{- 2} A^{2}] = [F V^{- 4} A^{2}]

JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Single correct option