Exercise

Difference between base quantities and derived quantities:                                                                    

1. Base quantities:

             Base quantities are the quantities based on which other quantities are expressed.

Seven physical quantities form the foundation for other physical quantities. These physical quantities are called the base quantities.

Example:

Length, mass, line, electric current, temperature, the intensity of light, and the derived quantities.

2. Derived quantities:

             The quantities that are expressed in terms of base quantities are called derived quantities.

Example:

Area, volume, speed, force, work, energy, power, electric charge, electric potential, etc.

Following are the base units among the given options:

kilogramme, mole, ampere, metre, Kelvin.

(a) Speed:

Speed = $\frac{\time{length}}{\time{time}}$

unit of speed = ms^-1

Base quantities involved in speed are metres and second.

(b) Volume:

Volume = length $\times$ width $\times$ height

Volume = m $\times$ m $\times$ m = m³

Base quantity involved in volume is metre.

(c) Force:

F = ma

1N = 1 kg $\times$ 1

1N = 1 kg

(d) Work:

Work done = Force × displacement

W = FS        ……… (i)

1J = 1N $\times$ 1 m

1J = 1 kg $\times$ 1 m

1J = 1 kg

Base quantities involved in work are kilogramme, metre, and second.

$ \begin{aligned} \text{Suppose my age} &= 15 \text{ years} \\ &= 15 × 365 = 5475 \text{ days } (\because \text{ 1 year = 365 days)} \\ &= 5465 × 24 = 131400 \text{ hours } (\because \text{1 day = 24 hours)} \\ &= 131400 × 60 = 7884000 \text{ minutes } (\because \text{1 hour = 60 minutes}) \\ &= 7884000 × 60 \boxed{= 473040000 \text{ seconds }} (\because \text{1 minutes = 60 second)} \end{aligned}$

1. SI unit is in use all over the world.
2. Manipulation in this system is quite easy i.e. the multiples and submultiples of the different units are obtained simply by multiplying or dividing with ten or powers of ten.

Least Count (LC)/ Vernier constant:

                 The difference between one small division on the main scale division and one on the Vernier scale division is 0.1 mm. it is called the most minor count (LC) of the Vernier Calipers.

Least count of Vernier Calipers can also be found as given below:

Least count of Vernier Calipers = $\frac{Smallest \: reading \: on \: main \: scale}{Number \: of \: decision \: on \: vernier \: scale}$

                                                  = $\frac{1mm}{10 \:Division}$ = 0.1 mm

                                           LC   =  0.1 mm = 0.01 cm 

Zero Error and Zero Correction:

         It is a defect in the measuring device (Vernier Calipers & Screw Gauge) & zero error is caused by an incorrect position of the zero point

For Example:

    To find the zero error, close the jaws of Vernier Calipers gently. If the zero line of the Vernier scale coincides with the zero of the main scale then the zero error is zero. Zero error will exist if the zero lines of the Vernier scale is not coinciding with the zero of the main scale.

When making some kind of scientific measurement. It is necessary to first check your instrument for ‘zero error’. The zero error is the reading displayed when you know the true reading should be exactly zero.

          For example, using a set of Vernier calipers, the zero is the reading that shows when the calipers are fully closed.

         As long as check for zero error, you can then use it to correct your readings.

Positive zero error:

          Zero error will be positive if the zero lines of the Vernier scale are on the right side of the zero of the main scale.

To get the correct value zero error must be recorded and subtracted from each reading.

Negative zero error:

          Zero error will be negative if the zero lines of the Vernier scale are on the left side of the zero of the main scale.

To get the correct value zero error must be recorded and added to each reading.

Stopwatch:

A stopwatch is used to measure the time interval of an event.

Mechanical stopwatch:

A mechanical stopwatch can measure a time interval up to a minimum of 0.1 seconds.

The least count of the mechanical stopwatch is 0.1 seconds.

Digital stopwatch:

Digital stopwatches commonly used in laboratories can measure a time interval as small as 1/100 second or 0.01 second.

The least count of the digital stopwatch is 0.01 seconds.

How to use a Stopwatch:

Use of a mechanical stopwatch:

A mechanical stopwatch has a knob that is used to wind the spring that powers the watch. It can also be used as a start-stop and reset button. The watch starts when the knob is pressed once. When pressed the second time, it stops the watch while the third press brings the needle back to zero position.                                                                                       

Use of a digital stopwatch:

          The digital stopwatch starts to indicate the time lapsed as the start/stop button is pressed. As soon as the start/stop button is pressed again. It stops and indicates the time interval recorded by it between the start and stop of an event. A reset button restores its initial zero settings.

LABORATORY SAFETY EQUIPMENT

A school laboratory must-have safety equipment such as:

• Waste-disposal basket
• Fire extinguisher. S
• Fire alarm.
• First Aid Box.
• Sand and water buckets.
• Fire blanket to put off the fire.
• Substances and equipment that need extra care must bear proper warning signs such as given below:

We need an extremely small interval of time “delta t” (∆t) as the smaller the time interval better resolution of the measurement is possible.

For example:

 In atomic/quantum physics especially reactions take place in a very short amount of time.

Significant figures:

          All the accurately known digits and the first doubtful digit in an expression are called significant figures. It reflects the precision of a measured value of a physical quantity.

 The accuracy in measuring a physical quantity depends upon various factors:

1. The quantity of the measuring instrument
2. The skill of the observer
3. The number of observations made

 For example, a student measures the length of a book as 18cm using a measuring tape. The numbers of significant figures in his/her measured value are two. The left digit 1 is the accurately known digit. While the digit 8 is the doubtful digit for which the student may not be sure.

Rules for determining significant figures:
The following rules help identify significant figures:

1. Non-zero digits are always significant.
2. Zeros between two significant figures are also significant.
3. Final or ending zeros on the right in the decimal fraction are significant.
4. Zeros are written on the left side of the decimal point to space the decimal point is not significant.
5. In whole numbers that end in one or more zeros without a decimal point. These zeros may or may not be significant. In such cases, it is not clear which zeros serve to locate the position value and which are parts of the measurement. In such a case, express the quantity using scientific notation to find the significant zero.

RULES TO FIND THE SIGNIFICANT DIGITS INA MEASUREMENT

• Digits other than zero are always significant.

 27 has 2 significant digits.

275 has 3 significant digits.

• Zeros between significant digits are also significant.

2705 has 4 significant digits.

• Final zero or zeros after the decimal are significant

 275.00 has 5 significant digits.

• Zeros used for spacing the decimal point are not significant here zeros are placeholders only.

 0.03 has 1 significant digit.    

0.027 has 2 significant digits.

ROUNDING THE NUMBERS

1. If the last digit is less than 5 then it is simply dropped. This decreases the number of significant digits in the figure.

For example,

1.943 is rounded to 1.94 (3 significant figures)

2. If the last digit is greater than 5, then the digit on its left is increased by one. This also decreases the number of significant digits in the figure.

For example,

1.47 is rounded to two significant digits 1.5

3. If the last digit is 5, then it is rounded to get nearest even number.

For example,

 1.35 is rounded to 1.4 and 1.45 is also rounded to 1.4

The greater the number of significant figures, the greater the precision. Each significant figure increases the precision by a factor of ten.

An improvement in the quality of measurement by using better instruments increases the significant figures in the measured result. The significant figures are all the digits that are known accurately and the one estimated digit. The more significant figure means greater precision.