Which of the following pairs has the same dim | vedclass

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(C) The dimension of the spring constant $k$ is given by $k = \frac{F}{x}$, so its unit is $\frac{N}{m} = \frac{kg \cdot m/s^2}{m} = kg \cdot s^{-2}$.

Vedclass · Accepted Answer

Spring constant and surface energy

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(C) The dimension of the spring constant $k$ is given by $k = \frac{F}{x}$, so its unit is $\frac{N}{m} = \frac{kg \cdot m/s^2}{m} = kg \cdot s^{-2}$. The dimensional formula is $[M L^0 T^{-2}]$.Surface energy is defined as energy per unit area: $	ext{Surface energy} = \frac{	ext{Energy}}{	ext{Area}} = \frac{J}{m^2} = \frac{N \cdot m}{m^2} = \frac{N}{m}$.Thus, the unit of surface energy is also $\frac{N}{m}$, which corresponds to the dimensional formula $[M L^0 T^{-2}]$.Since both have the same dimensional formula, option $C$ is correct.

Which of the following pairs has the same dimensions?

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