Question

Choose the option, whose pair doesn’t have same dimensions. (A) (Pressure × Volume) & Work done (B) (Force × Time) & Change in momentum (C) Kilocalorie & Joule (D) Angle & mole​

Answer 1

All the options given have the same dimensions.

Refer to the attachment.

Answer 2

All the pairs have similar dimensions.

Dimensional Formula:

It is the representation of quantities in the terms of seven fundamental quantities that are Mass, Length, Time, Temperature, Current, Luminous Intensity, Amount of substance.

Step-by-step explanation:

(A) Dimension of Pressure × Volume

                              $ML^{-1} T^{-2}$ × $L^{3}$

                           = $ML^{2}T^{-2}$

    Dimension of Work done = $ML^{2}T^{-2}$

(B) Dimension of  (Force × Time)

                          = $MLT^{-2$ × T

                          = $MLT^{-1}$

  Dimension of Change in Momentum

                         = $MLT^{-1}$

(C) Both kilocalorie and joule are units of heat therefore both have the same dimension i.e. $ML^{2} T^{-2}$

(D) Both Angle & Mole are dimensionless quantities.

Therefore, all the pairs here have the same dimensions.