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Question: In a view unit system, \[1\] unit of time is equal to \[10\] second, \[1\] unit of mass is \[5\,kg\]...

In a view unit system, 11 unit of time is equal to 1010 second, 11 unit of mass is 5 kg5\,kg and 11 unit of length is 20 m20\,m . In the new system of units 11 unit of energy is equal to:
A. 120J\dfrac{1}{{20}}J
B. 20J20J
C. 4J4J
D. 16J16J

Explanation

Solution

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 = [ML2T−2]\left[ {M{L^2}{T^{ - 2}}} \right]
Dimension of energy in new system = [5M×(20L)2×(10T)−2]\left[ {5M \times {{\left( {20L} \right)}^2} \times {{\left( {10T} \right)}^{ - 2}}} \right]
Value of energy in new system = New dimensionOld dimension\dfrac{\text{New dimension}}{\text{Old dimension}}
Value of energy in new system= 5×20×2010×10=20 J\dfrac{{5 \times 20 \times 20}}{{10 \times 10}} = 20\,J
So, in the new system, one unit of energy is 20 J20\,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 mm5000{\text{ }}mm , 500 cm500{\text{ }}cm , or 5 metres5{\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 mm45{\text{ }}mm rather than 4.5 cm4.5{\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.