Exercise 1(B) — Very Short Answer Type
Question 1
Define the least count of an instrument.
Answer
Least count of an instrument is the smallest measurement that can be taken accurately with it.
Question 2
How can you decrease the least count of a vernier callipers?
Answer
The least count of a vernier callipers can be decreased by:
1. increasing the number of divisions on the vernier scale.
2. decreasing the value of one division on main scale.
Question 3
Define the term 'Vernier constant'?
Answer
The term 'Vernier constant' is defined as the difference between the values of one main scale division and one vernier scale division. It is also known as least count of vernier.
Question 4
When is a vernier callipers said to be free from zero error?
Answer
On bringing, the movable jaw in contact with the fixed jaw, the zero mark of the vernier scale should coincide with the zero mark of the main scale. In this position, the tenth division of the vernier callipers coincides with the ninth division of the main scale.
If it is so, the vernier is said to be free from zero error.
Question 5
Name the part of the vernier callipers which is used to measure the following —
1. external diameter of a tube,
2. internal diameter of a mug,
3. depth of a small bottle,
4. thickness of a pencil.
Answer
1. External diameter of a tube — Outside jaws
2. Internal diameter of a mug — Inside jaws
3. Depth of a small bottle — Strip
4. Thickness of a pencil — Outer jaws
Question 6
State the difference between positive and negative zero error of a vernier callipers.
Answer
On bringing the two jaws of a vernier callipers together, if zero mark of the vernier scale is on the right of zero mark of the main scale, the zero error is said to be positive and if zero mark of the vernier scale is to the left of zero mark of the main scale, the zero error is said to be negative.
Question 7
Define the pitch of a screw gauge.
Answer
The pitch of a screw gauge is the linear distance moved by its screw on the main scale when the circular scale is given one complete rotation.
Question 8
State one use of a screw gauge.
Answer
A screw gauge is used to measure the diameter of a wire or thickness of a paper, etc.
Question 9
State the purpose of ratchet in a screw gauge.
Answer
The purpose of a ratchet in a screw gauge is to advance the screw by turning it till the object is gently held between the stud and the spindle of the screw.
Question 10
State the difference between positive and negative zero error of a screw gauge.
Answer
If on bringing the flat end of the screw in contact with the stud, the zero mark on the circular scale is below the base line of the main scale, the zero error is said to be positive and if the zero mark on the circular scale is above the base line of the main scale, the zero error is said to be negative.
Question 11
Name the instrument which can measure accurately the following —
1. the diameter of a needle,
2. the thickness of a paper,
3. the internal diameter of the neck of a water bottle,
4. the diameter of a pencil.
Answer
The given physical quantities can be measured accurately with the help of the following instruments —
1. the diameter of a needle — screw gauge.
2. the thickness of a paper — screw gauge.
3. the internal diameter of the neck of a water bottle — vernier callipers.
4. the diameter of a pencil — screw gauge.
Question 12
Which of the following measures a small length to a high accuracy — metre rule, vernier callipers, screw gauge?
Answer
A screw gauge measures a small length to a high accuracy.
Question 13
Name the instrument which has the least count —
1. 0.1 mm
2. 1 mm
3. 0.01 mm
Answer
The following instruments have the given least count —
1. 0.1 mm — vernier callipers
2. 1 mm — metre rule
3. 0.01 mm — screw gauge
Exercise 1(B) — Short Answer Type
Question 1
Explain the meaning of the term ‘least count of an instrument’ by taking a suitable example.
Answer
The least count of an instrument is the smallest measurement that can be taken accurately with it.
Example — The least count of a ruler is 1 mm, as there are 10 divisions between 0 and 1cm marks.
Question 2
A boy makes a ruler with graduation in cm on it (i.e., 100 divisions in 1 m). To what accuracy this ruler can measure ? How can this accuracy be increased ?
Answer
The ruler graduated by the boy, was having its zero mark at one end and 100 cm mark at the other end.
It had 100 subdivisions in one metre length, so the value of its one small division is 1 cm.
Thus, the ruler can be used to measure length accurately up to 1 cm.
In order to increase the accuracy, each cm should be further divided into 10 divisions so that the ruler can have a least count of 1 mm.
Question 3
A boy measures the length of a pencil and expresses it to be 2.6cm. What is the accuracy of his measurement? Can he write it as 2.60cm?
Answer
Given, the length of the pencil is 2.6 cm.
As the length is measured in cm till one place of decimal, we can assume that it was measured using a metre rule.
So, the measurement is accurate
No, it cannot be written as 2.60, as it would mean that length is measured precisely up to second decimal place using vernier callipers or a screw gauge.
Question 4
Define least count of a vernier callipers. How do you determine it?
Answer
The least count of a vernier callipers is equal to the difference between the values of one main scale division and one vernier scale division.
It is calculated as below —
Least count (L.C.)= Value of 1 main scale div−Value of 1 vernier scale div
Question 5
A vernier callipers has a zero error +0.06cm. Draw a neat labelled diagram to represent it.
Answer
vernier callipers with a zero error of +0.06 cm.
The least count of the vernier callipers shown in the diagram is 0.01 cm and the 6th division of the vernier scale, coincides with a main scale division.
∴,
Zero Error=6×L.C.Zero Error=6×0.01cm⇒Zero Error=0.06cm
Zero Error=6×L.C.
Zero Error=6×0.01cm
Zero Error=0.06cm
Hence, we get the zero error = 0.06 cm.
Question 6
State three uses of a vernier callipers.
Answer
Three uses of vernier callipers are as follows —
1. It is used to measure the length of a rod.
2. It is used to measure the diameter of a sphere.
3. It is used to measure the internal and external diameter of a hollow cylinder.
Question 7
Name the two scales of a vernier callipers and explain, how it is used to measure a length correct up to 0.01 cm.
Answer
The two scales of a vernier callipers are —
1. Main scale - it is fixed
2. Vernier scale – slides along the main scale.
The main scale is graduated to read up to 1mm and the vernier scale has the length of 10 divisions equal to the length of 9 divisions of main scale.
Value of 1 division of main scale (x) = 1mm.
Total number of divisions on the vernier scale (n) = 10
Using the formula given below,
Least count (L.C.)= Value of 1 main scale div (x)/total no. of div on vernier (n)
Least count (L.C.)=x/n
Least count (L.C.)=1mm/10
Least count (L.C.)=0.1mm
⇒Least count (L.C.)=0.01cm
Hence, a vernier callipers is used to measure a length accurately up to 0.01cm.
Question 8
Explain the terms —
(i) pitch, and
(ii) least count of a screw gauge.
How are they determined?
Answer
1. Pitch of a screw gauge — The pitch of a screw gauge is the linear distance moved by its screw on the main scale when the circular scale is given one complete rotation.
2. Least count of a screw gauge — Least count of a screw gauge is the linear distance moved by its screw along the main scale when the circular scale is rotated by one division on it.
The pitch and least count of the screw gauge are determined by using the formula —
Least Count=Pitch of screw gauge/Total no. of div on circular scale
Question 9
How can the least count of a screw gauge be decreased?
Answer
The least count can be decreased by —
1. Decreasing the pitch.
2. Increasing the total number of divisions on the circular scale.
Question 10
What do you mean by zero error of a screw gauge? How is it accounted for?
Answer
In an ideal case, when the flat end B of the screw is in contact with the stud A, and if the zero mark of circular scale coincide with the base line of main scale, the screw gauge is said to be free from zero error.
But sometimes, due to the mechanical error, on bringing the stud A in contact with stud B, the zero mark of the circular scale is either below or above the base line of the main scale, then the screw gauge is said to have a zero error.
There are two types of zero error —
1. Positive zero error and
2. Negative zero error.
The zero error is accounted by subtracting the zero error with its sign from the observed reading.
Correct reading = Observed reading - Zero error (with sign)
Question 11
A screw gauge has a least count 0.001 cm and zero error + 0.007 cm. Draw a neat diagram to represent it.
Answer
Below diagram shows a screw gauge with least count 0.001 cm and zero error + 0.007 cm:
Figure
Question 12
What is backlash error? Why is it caused? How is it avoided?
Answer
Sometimes, it is observed that on reversing the direction of rotation of the thimble, the tip of the screw does not start moving in the opposite direction at once, but it remains stationary for a part of rotation. This causes error in the observation which is called backlash error.
The reason for this is the wear and tear of threads of screw.
To avoid the error, while taking the measurements, screw should be rotated in one direction only.
If it is required to change the direction of rotation of screw then do not change the direction of rotation at once. Move the screw still further, stop there for a while and then rotate it in the reverse direction.
⇒.
