Question

If the unit of length and force be increased four times, then the unit of energy isA. increased 4 times.B. increased 8 times.C. increased 16 times.D. decreased 16 times.

Answer 1

Final Answer : C : Increased 16 times

I am Thinking that you are remaining in same system of unit (since you didn't mentioned new units) .

Steps:
1) We know,
Dim(E) = dim(F) * dim (L)
E(i) = F* L

Since, we are increasing F to 4 F and L to 4L.
So,
Energy will increase as 4 * 4 FL :16FL
Hence, Energy increases 16 times to that of initial.

Answer 2

Dimensionally, Force is represented as [MLT−2] and Length as [L].

⇒ Energy =Fd is represented as [MLT−2]×[L]=[ML2T−2].

Therefore, if Force and length are quadrupled in value, Energy =4[MLT−2]×4[L]=16[ML2T−2].

⇒ the unit of energy increased 16 times.