Vernier zero error sign confusion + is parallax angle for a star the full shift or half?

8 answers & replies

• [+][–]Farhan ShaikhDropperSample· 1mo ago

  For zero error, if the zero of the vernier is on the right of the main scale zero, it's positive zero error and you add it to the reading. So 2.34 + 0.05 = 2.39 cm.

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  • [+][–]Vivek Mishra12thSample· 1mo ago

    Bhai I think this is the other way round. Correction means we remove the error. If the instrument already shows +0.05 when nothing is between the jaws, then every reading has 0.05 extra in it. So we subtract. Ananya's 2.29 cm is right.

    Easy way I remember: positive error, so the instrument reads too much, so take away. Negative error, instrument reads too little, so add the magnitude. "True reading = observed reading - zero error", and you put the sign of the zero error in the formula. If the error is negative, minus a negative becomes plus.

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    • [+][–]Farhan ShaikhDropperSample· 1mo ago

      Ah right, I was thinking of "correction" and "error" as the same thing. Mixed up the words. Subtract it is, sorry.

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    • [+][–]Ananya Reddy11thSample· 1mo agoAuthor

      Subtract, got it. Writing "observed MINUS zero error (with sign)" in the pink box. Thank you all!

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• [+][–]Neel Chatterjee12thSample· 1mo ago

  Parallax: the angle you use is half the total shift, and the baseline is 1 AU. The star appears to shift back and forth against distant background stars over the year. The angle measured from the Sun to Earth's orbit radius as seen from the star is the parallax angle $\theta$, defined with the 1 AU radius as the baseline.

  Quick check of the number: $1\ \text{AU} = 1.496\times10^{11}$ m and $1'' = 4.85\times10^{-6}$ rad. So $D = \frac{b}{\theta} = \frac{1.496\times10^{11}}{4.85\times10^{-6}} \approx 3.08\times10^{16}\ \text{m}$ That's 1 parsec. About 3.26 light years.

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• [+][–]Nisha Verma12thSample· 1mo ago

  Exam-wise, learn all least counts as formulas:

  • Vernier: LC = 1 MSD - 1 VSD = (value of 1 main scale division) / (number of vernier divisions)
  • Screw gauge: LC = pitch / number of circular scale divisions
  • Pitch = distance moved on main scale per one full rotation

  For screw gauge the zero error rule is the same: true = observed - zero error (with sign). Practise 3-4 of these numericals with different signs and it becomes automatic. I did, in the Delhi heat with a desk fan, and haven't lost a mark on these since.

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• [+][–]Ishaan Bose11thSample· 1mo ago

  dumb question but why do we even use parallax for stars? can't we just use the light/radar thing

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  • [+][–]Arjun Nair12thSample· 1mo ago

    Radar or laser echo only works for nearby objects like the Moon or planets because the signal has to go there and come back. Stars are light years away so the echo would take years, and it would be too faint anyway. Parallax is just geometry and works for the nearer stars, then other methods take over for farther ones.

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