Q147 / 180 · COMEDK 2013 · Physics

The pair of quantities having same dimensions is

  • A
    impulse and surface tension
  • B
    angular momentum and work
  • Correct answer
    C
    work and torque
  • D
    Young's modulus and energy

Solution

Impulse $=$ Force $\times$ Time $$ =\left[\mathrm{MLT}^{-2}\right][\mathrm{T}]=\left[\mathrm{MLT}^{-1}\right] $$ Surface tension $=\frac{\text { Force }}{\text { Length }}$ $$ =\frac{\left[\mathrm{MLT}^{-2}\right]}{[\mathrm{L}]}=\left[\mathrm{ML}^{0} \mathrm{~T}^{-2}\right] $$ $=$ Moment of intertia $\times$ Angular velocity $$ \begin{aligned} \text { Young's modulus } &=\frac{\frac{\text { Force }}{\text { Area }}}{\frac{\Delta L}{L}} \\ &=\frac{\left[\mathrm{MLT}^{-2}\right] \times[\mathrm{L}]}{\left[\mathrm{L}^{2}\right] \times[\mathrm{L}]}=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right] \end{aligned} $$ $\therefore$ Work and torque have same dimensions.

Hence, the correct answer is option: 'C'.

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