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NEET
Exam
NEET
Subject
Physics
Chapter
Mathematics in Physics

NEET · Physics · Mathematics in Physics

The diameter of a sphere is measured using a screw gauge having a...

The diameter of a sphere is measured using a screw gauge having a pitch of 1 mm1\text{ mm} and 100100 divisions on its circular scale. If the measured diameter is 2.50 mm2.50\text{ mm}, the maximum percentage error in the calculated volume of the sphere will be:

Options

  1. A0.4%0.4\%
  2. B1.2%1.2\%
  3. C0.8%0.8\%
  4. D0.12%0.12\%

Correct answer

B. 1.2%1.2\%

Step-by-step solution

Least count of the screw gauge =PitchNumber of divisions=1 mm100=0.01 mm= \dfrac{\text{Pitch}}{\text{Number of divisions}} = \dfrac{1\text{ mm}}{100} = 0.01\text{ mm}.

This least count represents the absolute error in the measurement of the diameter, so Δd=0.01 mm\Delta d = 0.01\text{ mm}.

The volume of a sphere is given by V=43π(d2)3V = \dfrac{4}{3}\pi \left(\dfrac{d}{2}\right)^3.

The maximum percentage error in volume is:
ΔVV×100=3(Δdd)×100\dfrac{\Delta V}{V} \times 100 = 3 \left(\dfrac{\Delta d}{d}\right) \times 100

=3(0.012.50)×100=3×0.4%=1.2%= 3 \left(\dfrac{0.01}{2.50}\right) \times 100 = 3 \times 0.4\% = 1.2\%.

Answer: 1.2%1.2\%
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