Question

Certain amount of energy is measured as 400 units. If the fundamental units of length, mass and time, each are doubled the magnitude of the same energy in the new system will be ___units.

• A. 200
• B. 400
• C. 800
• D. 600

Answer 1

Answer: (A)

200

We need to find the dimensions of energy.

Energy stored in a system is equal to work done against a force $=Fx$ $=max$

Hence, the dimensions are $\left[M\right]\times \left[L{T}^{-2}\right]\times \left[L\right]=\left[M{L}^2{T}^{-2}\right]$

Hence, when fundamental units of $M,L,T$ are doubled, the fundamental unit of energy doubles, and hence the magnitude measured in those units halves.

Hence, correct answer is option A.