Question

Which of the following pairs of physical quantities have same dimension$?$

• A. force and work
• B. torque and energy
• C. torque and power
• D. force and torque

Answer 1

Answer: (B)

torque and energy

we know$,$ force $=$ mass $\times$ acceleration

energy $=$ Workdone $=$ force $\times$ displacement

power $=$ energy/time

torque $=$ force $\times$ perpendicular distance between force and axis of rotation$.$

now$,$ by these formula$,$ find dimension of all terms$.$

e.g., dimension of force $=\left[MLT⁻²\right]$

dimension of energy $=\left[ML²T⁻²\right]$

dimension of power $=\left[ML²T⁻³\right]$

dimension of torque $=\left[ML²T⁻²\right]$

Here it is clear that $,$ dimension of energy and dimension of torque are equal$.$

Hence,

option $\left(b\right)$ is correct$.$