Q38 / 92 · NTA Abhyas (JEE Main) 2020 · Physics · Units and Dimensions

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

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

Solution

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}

Hence, the correct answer is option: 'D'.

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