Question

Which of the following pair have same dimensional formula for both the quantities?
i) kinetic energy and torque
ii) resistance and inductance
iii) Young's modulus and pressure

• A. (i) only
• B. (ii) only
• C. (i) and (iii) only
• D. All the three

Answer 1

Answer: (D)

All the three

Dimension's of :

$\left(a\right)K.E=\left[M^1{L}^2{T}^{-2}\right]$

Torque $=\left[M^1{L}^2{T}^2\right]$

$\left(b\right)$ Resistance $=\left[M^{-1}{L}^2{T}^{-3}{A}^{-2}\right]$

Inductance $=\left[M^1{L}^2{T}^3{A}^{-2}\right]$

$\left(c\right)$ Young's Modulus. $E=\left[M^1{L}^{-1}{T}^{-2}\right]$

Pressure; $P=\frac{\left[Force\right]}{Area}$

$=\frac{\left[M^1{L}^1{T}^{-2}\right]}{\left[L^2\right]}$

$=\left[M^1{L}^1{T}^{-2}\right]$

$=\left[M^1{L}^{-1}{T}^{-2}\right]$

$\therefore$ All the $3$ have same Dimensional formula.