Question

Study the following.

List - I	List - II
a) Same negative dimensions of mass	I) Pressure, Rydberg constant
b) Same negative dimensions of length	II) Mangnetic induction field, Potential
c) Same dimensions	III) Capacity, Universal gravitational constant
d) Same dimension of current	IV) Energy density, Surface tension

• A. a-III, b-I, c-IV, d-II
• B. a-III, b-IV, c-I, d-II
• C. a-I, b-II, c-III, d-IV
• D. a-II, b-I, c-IV, d-III

Answer 1

Answer: (A)

a-III, b-I, c-IV, d-II

Pressure=$\frac{force}{area}=\frac{mass\times ac{c}^n}{area}=\frac{ML{T}^{-2}}{L^2}=M{L}^{-1}{T}^{-2}$

Unit of Rydberg constant $=L^{-1}$ ( These 2 quantities have same -ve dimension of length)

Surface tension $=M^1{L}^0{T}^{-2}$
Energy density $=$ Energy per unit area $=\frac{M{L}^2{T}^{-2}}{L^2}=M{L}^0{T}^{-2}$
$\to$(same dimensional formula)

Potential$=M{L}^2{T}^{-3}{A}^{-1}$
Magnetic induction field $=M{L}^2{A}^{-1}{T}^{-4}$(same dimension for current)