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Q.

Certain amount of energy measured in a system of units is 100 units. Now each of the fundamental units of that system is doubled. In the new units, the measured value of that energy will be

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a

200 new units

b

100 new units

c

25 new units

d

50 new units

answer is A.

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Detailed Solution

$n_{1} u_{1} = n_{2} u_{2}$
$n_{1} (M_{1} L_{1}^{2} T_{1}^{- 2}) = n_{2} (M_{2} L_{2}^{2} T_{2}^{- 2})$
$100 [\frac{M_{1}}{M_{2}} \frac{L_{1}^{2}}{L_{2}^{2}} \times \frac{T_{2}^{2}}{T_{1}^{2}}] = n_{2}$
$100 [\frac{M}{2 M} \times {(\frac{L}{2 L})}^{2} \times {(\frac{2 T}{T})}^{2}] = n_{2}$
$n_{2} = 50$

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