Question

what are the readings on the vernier scale in figures 14 a and b​

Answer 1

Answer:

From the figure, 0 of vernier callipers has gone past 3+0.3=3.3cm of main scale. Also, 6

th

division line of vernier scale matches with line of main scale.

So, total reading is 3.3+6×0.01=3.36cm

Answer 2

$\purple{\large{\underline{\underline{ \rm{Question:- }}}}}$

What are the readings on the vernier scales in figures 1.14a and 1.14b ?

$\sf{ \blue{How \: to \: use \: Vernier \: callipers:}}$

◈ Determine the pitch from the main scale.

◈ Determine the least count.

The least count of a Vernier can be determined by the following formula:

$\tt{L.C. = \dfrac{Pitch}{Number \: of \: V.S.D}}$

Thus, if the smallest value of main scale division i.e., Pitch = 1 mm and the number of V.S.D = 10 then,

$\tt{L.C. = \dfrac{1}{10} \: mm }$

$\tt{L.C. = 0.1 \: mm = 0.01 \: cm}$

◈ Hold the object tightly in the jaws $\sf{J_1}$ and $\sf{J_2}$.

◈ Determine the position of the zero of the vernier scale on the main scale and hence, find the value of length on the main-scale.

( The main scale reading is always smaller of the two values in which the zero of the vernier scale lies ).

◈ Now look for the vernier scale division, which coincides with any of the main scale divisions.

◈ Length of the object is found by the formula:

${ \underline{ \boxed{ \sf{Length = Reading \: on \: M.S + L.C \times V.S.D}}}}$

◈ Therefore, by following these steps we will find the length of an object.

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In the attachment they have asked readings on the vernier scale.

Fig 1.14a

Here, we just have to calculate the readings on the vernier scale. For calculating the readings on the vernier scales, we have to determine the least count then, we have to see for the vernier scale division, which coincides with any of the main scale division.

$\sf{ \blue{Let's \: find \: it:}}$

$\sf{L.C. = 0.1 \: mm \: (from \: above)}$

Now, look for the vernier scale division, which coincide with any of the main scale divisions. In figure 1.5, the 3rd division of the vernier scale coincides with the main scale.

We have:

$\sf{Reading \: on \: the \: vernier \: scale = p \times L.C.}$

Here p indicates V.S.D coinciding with M.S.

$\sf \therefore3 \times 0.1 = 0.3 \: mm$

Hence, the reading on the vernier scale of Fig. 1.14a = ${ \underline{ \boxed{ \sf{ 0.3 \: mm = 0.03 \: cm}}}}$

If we need to find Length of the object or reading shown by vernier scale, then we use formula:

$\sf{Reading \: shown \: by \: intrument = Main \: scale \: reading + L.C \times V.S.D}$

$\sf = Main \: scale \: reading + Vernier \: scale \: reading$

$\sf = 50.3 + 0.3$

$\sf = 50.6 \: mm = 5.06 \: cm \: (1 \: mm = 0.1 \: cm)$

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Fig. 1.14b

By using the same method here also we will calculate the reading on the vernier scale.

Now look for the vernier scale division, which coincides with the main scale division. In Fig. 1.14b, the 8th division of the vernier scale coincides with the main scale.

We have:

$\sf{Vernier \: reading = p \times L.C.}$

Here, p indicates Vernier scale division coinciding with main scale.

$\sf{ \therefore0.1 \times 8 = 0.8 \: mm}$

Hence, the reading on the vernier scale in Fig 1.14 b = $\underline{ \boxed{ \sf{0.8 \: mm = 0.08 \: cm }}}$

If we need to find the length of an object or the total reading which is shown by the vernier callipers, we use formula:

$\sf{Reading \: shown \: by \: instrument = Main \: scale \: reading + L.C \times V.S.D}$

$\sf = Main \: scale \: reading + Vernier \: scale \: reading$

$\sf = 90.6 + 0.8$

$\sf = 91.4 \: mm = 9.14 \: cm \: (1 \: mm = 0.1 \: cm)$

Note:

◎ M.S.D = Main scale division

◎ V.S.D = Vernier scale division

◎ M.S = Main scale

◎ V.S = Vernier scale

◎ L.C = Least count

$\Large{ \blue{ \sf{We \: are \: done!!}}}$

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