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  • Need explanation for: The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5mm and 100 respectively. When the scew gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below th

The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5mm and 100 respectively. When the scew gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the mean line.

The readings of the main scale and the circular scale, for a thin sheet, are 5.5mm and 48 respectively, the trhickness of this sheet is:

 

  • Option 1)

     

    5.740 mm

  • Option 2)

     

    5.725 mm

     

  • Option 3)

    5.950mm

  • Option 4)

    5.755 mm

Answers (1)

best_answer

 

To measure the thickness of the given sheet using screw gauge -

 

1.    Note the number of divisions on the circular scale.

2.    Give five complete rotations to the screw.

3.    Note the linear distance moved by the screw.

4.    Find the pitch and L.C. of screw gauge.

5.    Find the zero error and zero correction by moving the screw only in one direction in such a way that studs A and B just touch each other.

6.    Now grip the given sheet in the gap A and B of the screw gauge.

7.    Turn the screw head till the ratchet arrangement gives a click.

8.    Note the readings of linear scale and circular scale and find the observed thickness using the relation, observation thickness = L.S.R. + C.S.R.

9.    Add the zero correction to the observed thickness to find the corrected diameter.

10.    Repeat steps 6 to 9 to find the thickness from four more different places.

 

- wherein

C.S.R= circular \ scale \ reading

Total reading 

= M.S.R + C.S.R

= MSR +LC\times CSR

L.C = least count

C.S.R = Circular scale reading

 

A                B

m                2m

R                2R

TA                    TB

T = kinetic energy

So

V0 = orbital velocity = \sqrt{\frac{GM_{e}}{r}} = V

T = \frac{1}{2}mV_{0}^{2} = \frac{1}{2}mv^{2}

T_{A} = \frac{1}{2}m_{A}V_{A}^{2}

T_{B} = \frac{1}{2}m_{B}V_{B}^{2}

\frac{T_{A}}{T_{B}} = \frac{m_{A}}{m_{B}}\times \left ( \frac{V_{A}}{V_{B}} \right )^{2} = \frac{m}{2m}\times \left ( \frac{\frac{GM_{e}}{R}}{\frac{GM_{e}}{2R}} \right ) =1

\frac{T_{A}}{T_{B}} = 1

LC=\frac{Pitch}{Number\: \: of \: \: division}

LC=0.5\times 10^{-2}mm

+ve \: error\: =3\times 0.5\times 10^{-2}mm

                        =0.015\: mm

Reading = MSR + CSR - (+ ve error)

              = 5.5 + 0.24 - 0.015

             = 5.725 mm 


Option 1)

 

5.740 mm

Option 2)

 

5.725 mm

 

Option 3)

5.950mm

Option 4)

5.755 mm
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