Physical World Units and Measurements - Result Question 12
12. The pair of quantities having same dimensions is $\quad$ [NEET Kar. 2013]
(a) Young’s modulus and energy
(b) impulse and surface tension
(c) angular momentum and work
(d) work and torque
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Answer:
Correct Answer: 12. (d)
Solution:
- (d) Work $=$ Force $\times$ displacement
$=[MLT^{-2}][L]$
$=[ML^{2} T^{-2}]$
Torque $=$ Force $\times$ force arm
$ \begin{aligned} & =\text{ mass } \times \text{ acceleration } \times \text{ length } \\ & =[M] \times[LT^{-2}] \times[L]=[M L^{2} T^{-2}] \end{aligned} $
If dimensions are given, physical quantity may not be unique as many physical quantities have same dimensions. e.g., If the dimensional formula of a physical quantity is $[ML^{2} T^{-2}]$ it may be work or energy or torque.
