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Q)

If the unit of force and length each increased by 4 times , then the unit of energy is increased by

\[(a)\;16 \;times \quad (b)\;8\;times\quad (c)\;2\;times \quad (d)\;4\; times\]

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A)
Answer: 16 times.
Dimensionally, Force is represented as $ [MLT^{-2}]$ and Length as $[L]$.
$\Rightarrow$ Energy $ = F\;d$ is represented as $ [MLT^{-2}] \times [L] = [ML^2T^{-2}]$.
Therefore, if Force and length are quadrupled in value, Energy $ = 4[MLT^{-2}] \times 4[L] = 16[ML^2T^{-2}]$.
$\Rightarrow$ the unit of energy increased 16 times.
If the above questions options are
A)16%
B)1600%
C)1500%
D)400%
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