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Units and Measurements question

2025 · 24 Jan · Shift 1 · Q73
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Units and Measurements question

2025 · 24 Jan · Shift 1 · Q73

JEE MainPhysicsUnits and MeasurementsNumerical+4 / −1
The least count of a screw guage is 0.01 mm . If the pitch is increased by 75%75 \%75% and number of divisions on the circular scale is reduced by 50%50 \%50%, the new least count will be ‾×10−3 mm\underline{\hspace{2cm}}\times 10^{-3} \mathrm{~mm}​×10−3 mm
Numerical answer
View written solutionFree

Correct answer: 35

  1. Formula for least count of a screw gauge

The least count (L.C.) of a screw gauge is

L.C.=PitchNumber of divisions on circular scale\text{L.C.} = \frac{\text{Pitch}}{\text{Number of divisions on circular scale}}L.C.=Number of divisions on circular scalePitch​

Given initial least count:

L.C.1=0.01 mm\text{L.C.}_1 = 0.01\text{ mm}L.C.1​=0.01 mm

So initially,

PN=0.01\frac{P}{N} = 0.01NP​=0.01

where PPP = initial pitch and NNN = initial number of circular scale divisions.

  1. New pitch after increase of 75%75\%75%

If pitch is increased by 75%75\%75%,

P′=P(1+0.75)=1.75P=7P4P' = P(1+0.75)=1.75P=\frac{7P}{4}P′=P(1+0.75)=1.75P=47P​
  1. New number of divisions after reduction of 50%50\%50%

If the number of divisions is reduced by 50%50\%50%,

N′=N(1−0.50)=0.5N=N2N' = N(1-0.50)=0.5N=\frac{N}{2}N′=N(1−0.50)=0.5N=2N​
  1. New least count
L.C.2=P′N′=7P4N2\text{L.C.}_2 = \frac{P'}{N'} = \frac{\frac{7P}{4}}{\frac{N}{2}}L.C.2​=N′P′​=2N​47P​​ L.C.2=7P4⋅2N=72⋅PN\text{L.C.}_2 = \frac{7P}{4}\cdot \frac{2}{N} = \frac{7}{2}\cdot \frac{P}{N}L.C.2​=47P​⋅N2​=27​⋅NP​

But

PN=0.01 mm\frac{P}{N}=0.01\text{ mm}NP​=0.01 mm

Hence,

L.C.2=72×0.01=0.035 mm\text{L.C.}_2 = \frac{7}{2}\times 0.01 = 0.035\text{ mm}L.C.2​=27​×0.01=0.035 mm
  1. Express in the required form
0.035 mm=35×10−3 mm0.035\text{ mm} = 35 \times 10^{-3}\text{ mm}0.035 mm=35×10−3 mm

So the required integer is

35\boxed{35}35​
  1. Comparison with stored correct answer

Stored correct answer = 353535

Our derived answer = 353535

Hence, the answer agrees with the stored correct answer.

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