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The density of a solid ball is to be determined in an experime

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The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is $0.5 mm$ and there are 50 divisions on the circular scale. The reading on the main scale is $2.5 mm$ and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of $2%$ , the relative percentage error in the density is

0.9%

2.4%

3.1%

4.2%

Views: 5,467 students

Updated on: Feb 29, 2024

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Emily Discussed

The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is

0.5 mm

and there are 50 divisions on the circular scale. The reading on the main scale is

2.5 mm

and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of

2%

, the relative percentage error in the density is

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

Least count of screw gauge

= \frac{0.5}{50}

= 0.01 mm = Δ r

Diameter

r = 2.5 mm + 20 \times \frac{0.5}{50} = 2.70 mm

\frac{Δ r}{r} = \frac{0.01}{2.70}

Or \frac{Δ r}{r} \times 100 = \frac{1}{2.7}

Now density

d = \frac{m}{V} = \frac{m}{\frac{4}{3} π ( \frac{r}{2} ) ^{3}}

Here,

r

is the diameter.

∴ \frac{Δ d}{d} \times 100 = {\frac{Δ m}{m} + 3 (\frac{Δ r}{r})} \times 100 = \frac{Δ m}{m} \times 100 + 3 \times (\frac{Δ r}{r}) \times 100 = 2% + 3 \times \frac{1}{2.7} = 3.11%

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Question Text	The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is $0.5 mm$ and there are 50 divisions on the circular scale. The reading on the main scale is $2.5 mm$ and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of $2%$ , the relative percentage error in the density is
Updated On	Feb 29, 2024
Topic	Units and Measurements
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 7
Upvotes	679
Avg. Video Duration	6 min

Text solutionVerified

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