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# The value of 10 Joule in a system having $100 \mathrm{gm}, 10 \mathrm{cm}$ and $30 \mathrm{s}$ as fundamental units(A) $\quad \dfrac{1}{9 \times 10^{\circ}}$ (B) $\begin{array}{*{35}{l}} \text{ } & {{10}^{6}} \\\end{array}$ (C) $\begin{array}{*{35}{l}} \text{ } & 9\times {{10}^{6}} \\\end{array}$ (D) None of these

Last updated date: 21st Jun 2024
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Hint
It is known that the units which can neither be derived from other units nor they can be further resolved into simpler units are called fundamental units. Examples: Mass, length etc. Those units which can be expressed in terms of the fundamental units are called derived units. The International System of Units is the modern form of the metric system. A unit is the measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Based on this we have to solve this question.

Energy $=(1/2)\text{m}{{\text{v}}^{2}}$
so $\mathrm{E}$ is proportional to $\text{m}{{\text{v}}^{2}}$ .
$\text{E}=10\text{J}=10\text{Kg}{{(\text{m}/\text{s})}^{2}}$
$10\text{J}=10\text{Kg}{{(\text{m}/\text{s})}^{2}}=10\times 1000\text{g}\times {{(100\text{cm}/\text{s})}^{2}}$
$=10\times 10\times (100\text{g})\times {{(10\times 10\text{cm}/\text{s})}^{2}}$
$=100\times (100g)\times {{(10\times 30\times 10\text{cm}/30\text{s})}^{2}}$
$=100\times (100\text{g})\times {{(300\times 10\text{cm}/30\text{s})}^{2}}$
$=100\times {{(300)}^{2}}\times (100g){{(10cm/30s)}^{2}}$
$=9000000\times 100g{{(10\text{cm}/30\text{s})}^{2}}$
$=9000000$ new unit
$=9\times {{10}^{6}}$

Therefore, Option (C) is the correct answer.

Note
So, we can say that the use of a single unit of measurement for some quantity has obvious drawbacks. For example, it is impractical to use the same unit for the distance between two cities and the length of a needle. Thus, historically they would develop independently. One way to make large numbers or small fractions easier to read, is to use unit prefixes. At some point in time though, the need to relate the two units might arise, and consequently the need to choose one unit as defining the other or vice versa. For example, an inch could be defined in terms of a barleycorn. A system of measurement is a collection of units of measurement and rules relating them to each other.
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