Find the volume of the Sphere – Vernier Calipers.

2 Q : Find the volume of the given sphere using vernier calipers.

Ans:

Formula :

1. Volume of the Sphere V =  \frac{4}{3} \pi r^3 cm^3,

V= volume of Sphere, r = radius of  Sphere 
.

2.Least count of vernier calipers L.C = \frac{S}{N} cm,

S = value of 1 Main scale division , N = Number of vernier divisions.

3.Length (or) diameter  of Cylinder = Main scale reading (a) cm + ( n*L.C ) cm.

n = vernier coincidence .

Procedure : First we have to determine the least count count of the given vernier calipers.

To determine the volume of the  Sphere we have to determine the radius  (r) of the cylinder and substituting this value in the equation for the volume of the Sphere we can calculate it.

a) To determine the diameter of the Sphere : Given Sphere is held gently between jaws 1,1 of the vernier calipers.The reading on the main scale just before the zero of the vernier is noted.This is called Main scale reading (M.S.R).The number of division (n) on the vernier which coincides perfectly with any one of the main scale divisions is noted.This is called vernier coincidence (V.C).The vernier coincidence (V.C=n) is multiplied by least count to get the fraction of a main scale division.This is added to the main scale reading (M.S.R) to total reading or total diameter of the sphere.

Total reading = M.S.R + (V.C\times L.C)

Take the readings,keeping the Sphere between jaws 1,1 at different positions.Post the values of M.S.R and vernier coincidence (n) in the table.Take at least 5 readings, get the average of these 5 readings which is mean diameter (d)of the Sphere.

Place the Sphere diametrically between the jaws 1,1 of the vernier calipers, post the values of M.S.R and vernier coincidence (n) in the table. Take at least 5 readings, calculate the average of these readings which gives the mean diameter ( d=2r ) of the Sphere.

c) To determine the volume of the Sphere :Substituting the value mean radius ( r) of the sphere which is already determined, in the formula V = \frac{4}{3} \pi r^3 cm^3,

Determine Least count of vernier calipers : From the given vernier calipers

S= Length of Main scale division = 1 mm = 0.1 cm,

N = Number of vernier scale divisions = 10 ,

Substitute these values in the formula of Least count L.C = \frac{S}{N} = \frac{0.1}{10} =0.01 cm.

Table for  Diameter of the Sphere :

S.No M.S.R                acm Vernier Coincidence   (n) Fraction   b=n*L.C Total Reading (a+b) cm
1. 1.9 7 0.05 1.97
2. 1.9 6 0.04 1.96
3. 1.9 6 0.06 1.96
4. 1.9 7 0.05 1.97
5. 1.9 7 0.06 1.97

Average diameter of the sphere  d = 2r =  \frac{(1.97+1.96+1.96+1.97+1.97)}{5} cm = \frac{9.83}{5}

Average radius of the sphere r =\frac{d}{2} = \frac{1.966}{2}cm = 0.98 cm.

Observations :

Average radius of the cylinder r = 0.98 cm.

Calculations : Volume of the sphere V = \frac{4}{3} \pi r^3 cm^3 = \frac{4}{3}\times\frac{22}{7}\times(0.98)^3 cm^3

=3.94 cm^3

Precautions : 1) Take the M.S.R  and vernier coincide every time without parallax error.

2)Record all the reading in same system preferably in C.G.S system.

3) Do not apply excess pressure on the body held between the jaws.

4) Check for the ZERO error.When the two jaws of the vernier are in contact,if the zero division of the main scale coincides with the zero of the vernier scale no ZERO error will be there.If not ZERO error will be there, apply correction.

Result and Units : Volume of the sphere V = 3.94 cm^3.

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8 thoughts on “Find the volume of the Sphere – Vernier Calipers.

  1. Pingback: Contents 1 « A to Z of Physics

  2. thanks alot,
    but you can atleast insert one pic of the experiment showing the readings…it would be more helpful

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