JEE Main · PhysicsHard

$I f t h e u ni t so f l e n g t h, ma ss, an d t im e a r e d o u b l e d, t h e u ni t o f e n er g y b eco m es h o w man y t im es t h eor i g ina l u ni t ?$

Show correct answer & step-by-step solution

Correct answer: B — $$4$$

Solution

The dimensional formula for energy is

[M L^{2} T^{- 2}]

. Substituting the new units

M^{'} = 2 M

L^{'} = 2 L

, and

T^{'} = 2 T

, we get

E^{'} = (2 M) (2 L)^{2} (2 T)^{- 2} = 2 \times 4 \times (1/4) \times M L^{2} T^{- 2} = 2 E