if the unit of force and length each be increased by four then the unit of work is increased by
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16 times
W = F*D
W' = 4F*4D = 16FD = 16W
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Answer: 16 times.
Dimensionally, Force is represented as [MLT−2][MLT−2]and Length as [L][L].
⇒⇒ Energy =Fd=Fd is represented as [MLT−2]×[L]=[ML2T−2][MLT−2]×[L]=[ML2T−2].
Therefore, if Force and length are quadrupled in value, Energy =4[MLT−2]×4[L]=16[ML2T−2]=4[MLT−2]×4[L]=16[ML2T−2].
⇒⇒ the unit of energy increased 16 times.
Dimensionally, Force is represented as [MLT−2][MLT−2]and Length as [L][L].
⇒⇒ Energy =Fd=Fd is represented as [MLT−2]×[L]=[ML2T−2][MLT−2]×[L]=[ML2T−2].
Therefore, if Force and length are quadrupled in value, Energy =4[MLT−2]×4[L]=16[ML2T−2]=4[MLT−2]×4[L]=16[ML2T−2].
⇒⇒ the unit of energy increased 16 times.
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