Question

In a view unit system, \[1\] unit of time is equal to \[10\] second, \[1\] unit of mass is \[5\,kg\] and \[1\] unit of length is \[20\,m\] . In the new system of units \[1\] unit of energy is equal to:
A. $\dfrac{1}{{20}}J$
B. $20J$
C. $4J$
D. $16J$

Answer 1

Hint:A system of units is a collection of linked units used in calculations. Base units, which represent base dimensions, and derived units, which represent products of powers of base dimensions, make up the system. Some units are found in multiple systems of measurement.

Complete step by step answer:
A standard unit of measurement serves as a point of reference for describing objects based on their weight, length, or capacity. Despite the fact that measurement is a fundamental element of everyday life, children are unaware that there are many different ways to measure things. A standard unit of measurement is a quantifiable language that makes the relationship between the item and the measurement clear to everyone.

Now, coming to the question:
Dimension of energy = $\left[ {M{L^2}{T^{ - 2}}} \right]$
Dimension of energy in new system = $\left[ {5M \times {{\left( {20L} \right)}^2} \times {{\left( {10T} \right)}^{ - 2}}} \right]$
Value of energy in new system = $\dfrac{\text{New dimension}}{\text{Old dimension}}$
Value of energy in new system= $\dfrac{{5 \times 20 \times 20}}{{10 \times 10}} = 20\,J$
So, in the new system, one unit of energy is $20\,J$.

Hence, the correct option is B.

Note: The metric system provides many options for expressing a unit; for example, a unit can be represented as \[5000{\text{ }}mm\] , \[500{\text{ }}cm\] , or \[5{\text{ }}metres\]. As a result, huge numbers or trailing zeroes should be avoided because they make it difficult for people to count zeroes. Also, whenever possible, use whole numbers rather than decimal points, such as \[45{\text{ }}mm\] rather than \[4.5{\text{ }}cm\] , keeping in mind that a figure or phrase describing a single product or project must have uniformity in units. All units used must be in metres, centimetres, millimetres, and millimetres, for example.