Physics

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


ANSWER

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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