JEE Main Important Physics formulas
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Millimetres are measuring unit that is commonly used in mathematics. Engineers, surveyors, manufacturers, industrialists, and even school pupils utilise it. A millimetre is a length unit. In Latin, the prefix mill denotes a thousand. As a result, one mm equals one-thousandth of a metre. Here are some other important items to remember:
Millimetres are represented by the sign mm.
One centimetre equals ten millimetres.
A millimetre equals 1000 micrometres.
One millimetre equals one million nanometers.
1 inch equals 25.4 millimetres.
A millimetre equals 0.03937 inches.
The metre is defined as the length of light's passage in a vacuum over some time of 1/299792458 of a second. This meaning has been used since 1983, however, it was first documented in French in 1800-10.
A millimetre is one-thousandth of a metre. As a result, a millimetre is defined as the distance travelled by light in 1/299792458000 of a second. It is also known as 'mili' and is symbolised as mm. The term ‘mili’ perplexes Americans because it typically refers to a thousandth of an inch. A millimetre is equal to 0.03937 of an inch.
A centimetre is a metric measurement unit used to determine the length of an object. It is written in centimetres.
· A metre is 100 centimetres long.
· One centimetre is equal to 10 millimetres.
· The centimetre is abbreviated as cm.
· When computing an object's surface area, the unit of measurement becomes cm2.
· When determining the volume of an item, the unit of measurement changes to cm3.
The two most common measuring instruments are:
1. Ruler: The most frequent measurement instrument in mathematics is a ruler. It is used to measure the length of little items such as notebooks, pencils, and bottles. Most rulers provide two measuring units: centimetres and inches. A ruler typically has 15 or 30 cm.
2. A metre stick is a measuring implement that measures one metre (one hundred centimetres) and is used to measure objects in metres and millimetres. A metre stick can be used to measure things like the length of a table or the breadth of a bag.
Metric conversions are simple to grasp, as is their connection to other units of measurement.
One mm, for example, is equal to 0.1 cm. However, one centimetre equals ten millimetres.
When we express it in the form of an equation, we get-
1 cm equals 10 mm, and
1 mm = 0.1 cm
Example 1. How many millimetres are in 5 centimetres?
Ans, The above problem can be solved as follows
\begin{aligned}
&\text{Five Centimeters} = \text{Five} \times \text{One Centimeter}\\
\\
&\text {But,}\\
&\text{One Centimetre = Ten Milimetres}\\
&\text{1mm = 10cm}\\
\\
&\text{Therefore}\\
&\text{Five Centimetres} = \text{Five} \times \text{Ten Millimetres}\\
&\text{Five Centimetres} = 5 \times 10\text{mm}\\
&\text{Five Centimetres}= 50\text{mm}
\end{aligned}
Example 2. How many millimetres are in 17 metres?
Ans. The above question can be solved as follows
Let us first find how many millimetres is a metre. This can be done as follows
\begin{aligned}
&\text{One Centimmetre} = \text{Ten Millimetres}\\
&\text{One Metre} = \text{Hundred Centimetres}\\
\\
&\text{Therefore,}\\
&\text{One Metre} = 100 \times \text{One Centimetre}\\
&\text{One metre}=100 \times \text{Ten Millimetres}\\
&\text{One Metre}=100 \times 10\text{mm}\\
&1\text{m} = 1000\text{mm}
\end{aligned}
Now let's solve the question
\begin{aligned}
&\text {Seventeen Metres} = \text{Seventeen} \times \text{One Metre}\\
&17\text{mm} = 17 \times 1\text{m}\\
\\
&\text{But we know that,}\\
&1\text{m} = 1000\text{mm}\\
\\
&\text{By substituting we will find,}\\
&17\text{m} = 17 \times 1000\text{mm}\\
&17\text{m} = 17000\text{mm}\\
\end{aligned}
Example 3. How many centimetres are in 25 millimetres?
Ans. The above question can be solved as follows
\begin{aligned}
&\text{One Centimetre} = \text{Ten Millimetres}\\
&1\text{cm} = 10\text{mm}\\
\\
&\text{by cross multiplication we can also say that,}\\
&1\text{mm}=\frac{1}{10}\text{cm}\\
\\
&\text{Twenty Five Milimetres} = \frac{\text{Twenty Five }}{10} \text{Centimetres}\\
&25\text{mm} = \frac{25}{10}\text{cm}\\
&25\text{mm}=2.5\text{cm}
\end{aligned}
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