Physics

If the units of $M$ and $L$ are increased four times, then the unit of energy will be increased by:-

16 times

SOLUTION
Dimensionally$,$ force is represented as $\left[ {ML{T^{ - 2}}} \right]$ ans length as $\left[ L \right].$
$\Rightarrow$ Energy $=Fd$ is represented as $\left[ {ML{T^{ - 2}}} \right] \times \left[ L \right] = \left[ {M{L^2}{T^{ - 2}}} \right].$
Therefore$,$ if force and length are quadrupled in value$,$
Energy$=4\left[ {ML{T^{ - 2}}} \right] \times 4\left[ L \right] = 16\left[ {M{L^2}{T^{ - 2}}} \right].$
$\Rightarrow$ the unit of energy increased $16$ times$.$
Hence,
option $(A)$ is correct answer.

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Single Correct Medium Published on 18th 08, 2020
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