Question

If the units of length and force are increased by four times the units of energy will be increased by

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{E}=\mathrm{F}.\mathrm{ds} \\ \mathrm{Dimension}\mathrm{of}\mathrm{F}=\left[{\mathrm{MLT}}^{-2}\right] \\ \mathrm{dimension}\mathrm{of}\mathrm{ds}=\left[\mathrm{L}\right] \\ \mathrm{E}=\left[{\mathrm{MLT}}^{-2}\right]\left[\mathrm{L}\right] \\ \mathrm{E}=\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right] \\ \mathrm{When}\mathrm{force}\mathrm{and}\mathrm{length}\mathrm{increased}\mathrm{by}4\mathrm{times}, \\ \mathrm{F}=4\left[{\mathrm{MLT}}^{-2}\right] \\ \mathrm{ds}=4\left[\mathrm{L}\right] \\ \mathrm{E}\text{'}=4\left[\mathrm{MLT}{-}^2\right]\times 4\left[\mathrm{L}\right] \\ \mathrm{E}\text{'}=16\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right] \\ \mathrm{E}\text{'}=16\mathrm{E} \end{gathered}$$