Aim: Using Vernier Callipers to find
1. The Volume of the given sphere with that mass of the sphere.
2. The length of the given cylinder.
3. The length and breadth of the glass plate.
Apparatus:
Vernier Callipers, Sphere, Cylinder and Glass plate.
Formula:
1. The volume of the given sphere
\[V=\frac{4}{3}.\pi. r^{3} (cm^{3})\]
\[Where\; r=\frac{d}{2} = radius\;of \; the \; bob\; (cm).\; d= diameter\; of\; the\; sphere\; (cm.)\]
\[m=V.\rho \; (gm)\]
\[Where \; \rho = density\; of \; the \; sphere\;(gm/cm^{3})\]
3. Radius of the sphere (r), lenth(l) of the cylinder and length (l'), breadth(b) of the glass plate from
Average radius of the sphere
\[r=\frac{1.93}{2}=0.965 \;cm\]
Mass of the Brass sphere
Volume of the sphere \[V=3.753\;(cm)^3\]
Given density of the brass sphere \[\rho =8.4 \;gm/(cm)^3\]
To determine the length of a cylinder
7. As shown in figure grip the given cylinder in between the two jaws c and d such that its length parallel to length of main scale. then take M.S.R and V.C readings as above.
8. Determine the length of cylinder from total reading = M.S.R + (V.C X L.C).
9. Repeat the experiment 6 times by keeping the cylinder in different positions and tabulate the readings in the table 2 and calculate the average length(l) of the cylinder.
Vernier Callipers total reading = M.S.R + (V.C X L.C) (cm)
4. Vernier Callipers
\[L.C = \frac{1 MSD}{N}\;(cm)\]
Procedure:
Least countof vernier callipers:
1. Note the value of one main scale division(1MSD) and the number of the divisions on the vernier scale N. vernier callipers least count(L.C) is determined as
\[L.C = \frac{1 MSD}{N}\;(cm)\]
To determine the radius of a sphere
2. As shown in figure grip the given sphere in between the two jaws c and d. then note the reading on the main scale just before the zero division of the vernier scale as main scale reading(MSR) and the vernier scale division which coincides with one of the amain scal divisions as vernier coincidense V.C(n).
3. Determine the diamter of the sphere from totla reading = M.S.R +(V.C X L.C)
4. Repeat the experiment 6 times by kepping the sphere in different positions and tabulate the readings in the table 1 and calculate average diamter of the sphere(d) with that radius of the sphere as r =d/2.
5. by substituting above value radius(r), volume of the sphere is calculated as
\[V=\frac{4}{3}.\pi. r^{3} (cm^{3})\]
6. Mass of the given sphere is calculated as
\[m=V.\rho \; (gm)\]
Table:1 To find radius of the cylinder(l)
L.C = 0.01 cm
S.No
|
Main Scale Reading (M.S.R)
a (cm)
|
Vernier Coincidence(n)
|
Extra fraction
b=n X L.C
|
Total Reading
a + b (cm)
|
1.
|
1.9
|
3
|
0.03
|
1.93
|
2.
|
1.9
|
4
|
0.04
|
1.94
|
3.
|
1.9
|
2
|
0.02
|
1.92
|
4.
|
1.9
|
4
|
0.04
|
1.94
|
5.
|
1.9
|
3
|
0.03
|
1.93
|
6.
|
1.9
|
2
|
0.02
|
1.92
|
Calculations:
Average diameter of
the sphere
\[d= \frac{1.93+1.94+1.92+1.94+1.93+1.82}{6}=\frac{11.58}{6}=1.93 \;cm\]
Average radius of the sphere
\[r=\frac{1.93}{2}=0.965 \;cm\]
Volume of the Sphere
\[V= \frac{4}{3}.\pi .r^{3}\;(cm^3)\]
\[V= \frac{4}{3}.\pi .r^{3}\;(cm^3)\]
\[V= \frac{4}{3}X 3.141X(0.965)^3\]
\[V= \frac{4}{3}X 3.141X(0.965)X(0.965)X(0.965)\]
\[V=3.753\;(cm)^3\]
Volume of the sphere \[V=3.753\;(cm)^3\]
Given density of the brass sphere \[\rho =8.4 \;gm/(cm)^3\]
Mass of the brass sphere \[m=V.\rho \; (gm)\]
\[m =(3.753)X(8.4)\]
\[m = 31.5252\;gm\]
To determine the length of a cylinder
7. As shown in figure grip the given cylinder in between the two jaws c and d such that its length parallel to length of main scale. then take M.S.R and V.C readings as above.
8. Determine the length of cylinder from total reading = M.S.R + (V.C X L.C).
9. Repeat the experiment 6 times by keeping the cylinder in different positions and tabulate the readings in the table 2 and calculate the average length(l) of the cylinder.
Table:2 To find length of the cylinder(l) L.C = 0.01 cm
S.No
|
Main Scale Reading (M.S.R)
a (cm)
|
Vernier Coincidence(n)
|
Extra fraction
b=n X L.C
|
Total Reading
a + b (cm)
|
1.
|
2.2
|
5
|
0.05
|
2.25
|
2.
|
2.2
|
4
|
0.04
|
2.24
|
3.
|
2.2
|
5
|
0.05
|
2.25
|
4.
|
2.2
|
6
|
0.06
|
2.26
|
5.
|
2.2
|
4
|
0.04
|
2.24
|
6.
|
2.2
|
5
|
0.05
|
2.25
|
Calculations:
Average length of the cylinder
\[l= \frac{2.25+2.24+2.25+2.26+2.24+2.25}{6}=\frac{13.49}{6}=2.25 \;cm\]
To determine teh length(l) and breadth (b) of the glass plate:
10. As shown in figure grip the given glass plate in between the jwo jaws c and d such that its length parallel to length of main scale. then take M.S.R and V.C readings as above.
11. Determine the length of glass plate from total reading = M.S.R + (V.C X L.C).
12. Repeat the experiments 6 times by keeping teh glass plate in different positions and tabulate teh readings in tah table 3 and calculated the average length (l) of teh glass plate.
13. Similarly find the breadth of the glass plate by tabulating the readings in table 4.
To determine teh length(l) and breadth (b) of the glass plate:
10. As shown in figure grip the given glass plate in between the jwo jaws c and d such that its length parallel to length of main scale. then take M.S.R and V.C readings as above.
11. Determine the length of glass plate from total reading = M.S.R + (V.C X L.C).
12. Repeat the experiments 6 times by keeping teh glass plate in different positions and tabulate teh readings in tah table 3 and calculated the average length (l) of teh glass plate.
13. Similarly find the breadth of the glass plate by tabulating the readings in table 4.
Table:3 To find length of the glass plate(l') L.C = 0.01 cm
S.No
|
Main Scale Reading (M.S.R)
a (cm)
|
Vernier Coincidence(n)
|
Extra fraction
b=n X L.C
|
Total Reading
a + b (cm)
|
1.
|
6.8
|
2
|
0.02
|
6.82
|
2.
|
6.8
|
4
|
0.04
|
6.84
|
3.
|
6.8
|
3
|
0.03
|
6.83
|
4.
|
6.8
|
4
|
0.04
|
6.84
|
5.
|
6.8
|
2
|
0.02
|
6.82
|
6.
|
6.8
|
3
|
0.03
|
6.83
|
Calculations:
Average length of the glass plate
\[l'= \frac{6.82+6.84+6.83+6.84+6.82+6.83}{6}=\frac{40.98}{6}=6.83 \;cm\]
Table:4 To find breadth of the glass plate(b) L.C = 0.01 cm
S.No
|
Main Scale Reading (M.S.R)
a (cm)
|
Vernier Coincidence(n)
|
Extra fraction
b=n X L.C
|
Total Reading
a + b (cm)
|
1.
|
3.1
|
6
|
0.06
|
3.16
|
2.
|
3.1
|
5
|
0.05
|
3.15
|
3.
|
3.1
|
7
|
0.07
|
3.17
|
4.
|
3.1
|
6
|
0.06
|
3.16
|
5.
|
3.1
|
7
|
0.07
|
3.17
|
6.
|
3.1
|
5
|
0.05
|
3.15
|
Calculations:
Average breadth of the glass plate
\[b= \frac{3.16+3.15+3.17+3.16+3.17+3.15}{6}=\frac{18.96}{6}=3.16 \;cm\]
Precautions:
1. Take the readings without parallax error.
2. The object should be gripped tightly between the two jaws.
Observations:
1.The value of 1 M.S.D(S) = 0.1 cm.
2. The number of lvernier calliper scale divisions (N) = 10 no units.
3. Vernier callipers least count (L.C) = 0.01 cm.
4. Average radius of lthe sphera (r) = 0.965 cm.
Results:
1. Volume of the given sphere \[V=3.753\;(cm)^3\].
2. MAss of teh given sphere \[m = 31.5252\;gm\].
3. Average length of the cylinder \[l=2.25 \;cm\].
4. Average length of the glass plate\[l'=6.83 \;cm\].
5. Average breadth of the glass plate \[b=3.16 \;cm\].
Precautions:
1. Take the readings without parallax error.
2. The object should be gripped tightly between the two jaws.
Observations:
1.The value of 1 M.S.D(S) = 0.1 cm.
2. The number of lvernier calliper scale divisions (N) = 10 no units.
3. Vernier callipers least count (L.C) = 0.01 cm.
4. Average radius of lthe sphera (r) = 0.965 cm.
Results:
1. Volume of the given sphere \[V=3.753\;(cm)^3\].
2. MAss of teh given sphere \[m = 31.5252\;gm\].
3. Average length of the cylinder \[l=2.25 \;cm\].
4. Average length of the glass plate\[l'=6.83 \;cm\].
5. Average breadth of the glass plate \[b=3.16 \;cm\].
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