JEE Main · PhysicsHard

$If the units of length, mass, and time are doubled, the unit of energy becomes n times the original unit. Find the value of n .$

A. $2$
B. $4$
C. $8$
D. $16$

Show correct answer & step-by-step solution

Correct answer: B — $4$

Solution

Energy has dimensions of [M L^{2} T^{- 2}] . Given M^{'} = 2 M, L^{'} = 2 L, and T^{'} = 2 T, the new unit E^{'} is E^{'} = (2 M) (2 L)^{2} (2 T)^{- 2} = 2 M \cdot 4 L^{2} \cdot \frac{1}{4} T^{- 2} = 2 M L^{2} T^{- 2} = 2 E . Thus, n = 2 .

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