If unit of length, mass and time each be doubled, the new unit of work done is _____ times the old unit of work

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If unit of length, mass and time each be doubled, the new unit of work done is _____ times the old unit of work

PhysicsUnits and DimensionsJEE Main

Options:

A $4$
B $6$
C $8$
D $2$

Solution:

2203 Upvotes Verified Answer

The correct answer is:

2

n_{2} = n_{1} {[\frac{M_{2}}{M_{1}}]}^{1} {[\frac{L_{2}}{L_{1}}]}^{2} {[\frac{T_{2}}{T_{1}}]}^{- 2}

Given,

M_{2} = 2 M_{1}, L_{2} = 2 L_{1}, T_{2} = 2 T_{1}

∴ n_{2} = n_{1} {[2]}^{1} {[2]}^{2} {[2]}^{- 2} = 2 n_{1}

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