Q96 / 180 · NEET 2013 (Karnataka) · 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

(1) $$ \begin{aligned} \text { Torque }=\text { F.S. } & =\left[\mathrm{MLT}^{-2}\right][\mathrm{L}] \\ & =\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right] \end{aligned} $$ correct option is (3) (2) Angular moment $=$ M.I. $\times$ angular velocity $$ \begin{aligned} =\left[\mathrm{ML}^2\right]\left[\mathrm{T}^{-1}\right] & =\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right] \\ \text { Work }=F . S . & =\left[\mathrm{MLT}^{-2}\right][\mathrm{L}] \\ & =\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right] \end{aligned} $$ (3) Work $=\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$ from Related Theory (1) $$ \begin{aligned} & \text { Impluse }=\text { force } \times \text { time } \\ &=\left[M L T^{-2}\right][T]=\left[M L T^{-1}\right] \\ & \text { Surface tension }=\frac{\text { Force }}{\text { length }}= \\ & \frac{\left[M L T^{-2}\right]}{[L]}=\left[M T^{-1}\right] \end{aligned} $$

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

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