Physics

A physical quanity $$P$$ is releated to four observation $$a,b,c$$ and $$d$$ as follows $$P=a^{3}b^{3}/\surd cd$$The percentage errors of measurement in $$a,b,c$$ and $$1\%,3\%,4\%$$ and $$2\%$$ repectively. What is the percentage erros in quanity $$P$$? If the value of $$P$$. Calculated using the above relations turns out to +ve $$3.763$$, to what value you should round off the result?


SOLUTION

Dfractional error in P is

$$ \dfrac{\Delta P}{P}=\left[ 3\dfrac{\Delta a}{a}+3\dfrac{\Delta b}{b}+\dfrac{1}{2}\dfrac{\Delta c}{c}+\dfrac{\Delta d}{d} \right] $$

 $$ \dfrac{\Delta P}{P}=\left[ \dfrac{3}{100}+\dfrac{9}{100}+\dfrac{2}{100}+\dfrac{2}{100} \right] $$

 $$ \dfrac{\Delta P}{P}=\dfrac{16}{100}=0.16 $$

Percentage error on $$P=\dfrac{\Delta P}{P}\times 100=16\,\,$$%

It is given that $$P=3.763$$

So the round off value is 3.8

View Answers

You're just one step away

Create your Digital Resume For FREE on your name's sub domain "yourname.wcard.io". Register Here!


Subjective Medium Published on 18th 08, 2020
Next Question
Questions 244531
Subjects 8
Chapters 125
Enrolled Students 201
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
Dimensions of strain are
  • A. $$MLT^{-1}$$
  • B. $$ML^2T^{-1}$$
  • C. $$MLT^{-2}$$
  • D. $$M^0L^0T^{0}$$

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer
Q2 Single Correct Medium
The dimensional formula for impulse is:
  • A. $${ MLT }^{ -2 }$$
  • B. $${ MLT }^{ -1 }$$
  • C. $${ ML }^{ 2 }{ T }^{ -1 }$$
  • D. $${ M }^{ 2 }{ LT }^{ -1 }$$

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer
Q3 TRUE/FALSE Medium
SI unit of energy is joule .
  • A. True
  • B. False

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer
Q4 Single Correct Medium
The dimensions of $$CV^2$$ matches with the dimensions of
  • A. $$L^2 I$$
  • B. $$L^2 I^2$$
  • C. $$L I^2$$
  • D. $$\dfrac{1}{LI}$$

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer
Q5 Single Correct Medium
The dimensions of heat capacity is:
  • A. $$[L^2T^{-2}\theta^{-1}]$$
  • B. $$[ML^2T^{-2}\theta^{-1}]$$
  • C. $$[M^{-1}L^2T^{-2}\theta^{-1}]$$
  • D. None of these

Asked in: Physics - Units and Measurement


1 Verified Answer | Published on 18th 08, 2020

View Answer