please solve this with proper explanation I will mark brainliest if the answer and the working along with explanation is correct
Answers
Answer:
Explanation:
Now, let us use this Vernier calipers to measure the diameter D of a marble ball (marble balls usually have D = 1/2 in). The measurement is shown in the figure 2. Here, xm0 is the distance between the jaw attached to main scale (left jaw) and the 0th mark on the main scale and xv0 is the distance between the jaw attached to Vernier scale (right jaw) and the 0th mark on the Vernier scale. Observe that the diameter is given by
D
=
x
m
0
+
x
where x is the distance between the 0th mark on the main scale and the right jaw.
Now, note that the 7th mark on Vernier scale coincides with 1.9 cm on the main scale. This point is called the point of coincidence. The distance between the 0th mark on main scale and the point of coincidence is xm and the distance between the 0th mark on Vernier scale and the point of coincidence is xv. Thus,
x
+
x
v
0
+
x
v
=
x
m
Substitute x from above equation into the first equation to get
D
=
(
x
m
−
x
v
)
−
(
x
m
0
−
x
v
0
)
The quantity (
x
m
0
−
x
v
0
) is called the zero error of the Vernier calipers. Negative of the zero error is called zero correction. Note that
x
m
0
=
x
v
0
in a Vernier calipers without zero error (which is true in this case). Also,
x
m
=
19
M
S
D
=
19
mm and
x
v
=
7
V
S
D
=
7
(
9
/
10
)
=
6.3
mm. Substitute these values in above equation to get D = 12.7 mm =1.27 cm (half inch marble).
Figure 2: Measuring Diameter of a Marble Ball
There is another easier way to get the measured value. The main scale reading (MSR) is the first reading on the main scale immediately to the left of the zero of Vernier scale (MSR = 12 mm in this example). The Vernier scale reading (VSR) is the mark on Vernier scale which exactly coincides with a mark on the main scale (VSR = 7 in this example). Note that there are VSR divisions on the main scale between MSR mark (i.e., mark on the main scale immediately to the left of the zero of the Vernier scale) and the point of coincidence. Thus,
x
v
=
V
S
R
×
V
S
D
,
x
m
=
M
S
R
+
V
S
R
×
M
S
D
Corresponding values of the parameters for the zero errors are
x
v
0
=
V
S
R
0
×
V
S
D
,
x
m
0
=
M
S
R
0
+
V
S
R
0
×
M
S
D
Substitute in the expression for D to get
D
=
M
S
R
+
V
S
R
×
L
C
−
Z
e
r
o
E
r
r
o
r
where LC = MSD - VSD is called the least count or Vernier constant. It is the smallest length that can be measured accurately with a Vernier calipers. For the given Vernier calipers
L
C
=
M
S
D
−
V
S
D
=
1
−
9
/
10
=
0.1
m
m
,
D
=
M
S
R
+
V
S
R
×
L
C
=
12
+
7
(
0.1
)
=
1.27
m
m
Note that Vernier calipers can be used to measure (1) outer dimensions like diameter of a sphere or edge of a cube (2) inner dimensions like inner diameter of a hollow cylinder and (3) depth of a hollow cylinder.