Tag: measurement of length

Questions Related to measurement of length

A physical quantity $Q$ is calculated according to the expression
$Q =\dfrac{A^3B^3}{C\sqrt D}$
If percentage errors in $A, B, C, D$ are $2\%, 1\%, 3\%$ and $4\%$ respectively. What is the maximum percentage error in $Q$?

physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

  1. $\pm\ 8\%$

  2. $\pm\ 10\%$

  3. $\pm\ 14\%$

  4. $\pm\ 12\%$

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Correct Option: C

If maximum percentage errors in measurement of length, mass and time are 2%,1% respectively then maximum percentage error in kinetic energy will be 

physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

  1. 1 %

  2. 4 %

  3. 7 %

  4. 5 %

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Correct Option: A

In an experiment measurements of velocity of an object $\left( {in\;m{s^{ - 1}}} \right)$ are 342,33,318 and 322.The mean absolute error in the measurement is 

physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

  1. 8 $m{s^{ - 1}}$

  2. 4 $m{s^{ - 1}}$

  3. 10 $m{s^{ - 1}}$

  4. 12 $m{s^{ - 1}}$

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Correct Option: C

Measurement of two physical quantities are given as 
$x = \left( {4.0\; \pm \;0.4} \right)\;m{s^{ - 1}}$
$Y = \left( {1.0\; \pm \;0.1} \right)\;s$
The value of XY will be.

physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

  1. $\left( {4.0\; \pm \;0.8} \right)\;m$

  2. $\left( {4.0\; \pm \;0.5} \right)\;m$

  3. $\left( {4.0\; \pm \;0.3} \right)\;m$

  4. $\left( {4.0\; \pm \;0.4} \right)\;m$

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Correct Option: A

The maximum error in the measurement of mass and density of a cube are 3% and 1% respectively. The maximum error in the measurement of volume will be:

physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

  1. 1%

  2. 2%

  3. 3%

  4. 4%

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Correct Option: D
Explanation:

$\displaystyle V=\frac {m}{d}$

$\displaystyle \frac {\Delta V}{V}\times 100=(\frac {\Delta m}{m}+\frac {\Delta d}{d})\times 100=(3+1)=4$%

The time period of oscillation of simple pendulum given by $T = 2\pi\sqrt{\frac{L}{g}}$ where $L= (200 \pm 0.1) cm$. The time period, T =4s and the time of 100 oscillations is measured using a stopwatch of least count 0.1 s. The percentage error in g is

physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

  1. $0.1$%

  2. $1.5$%

  3. $2$%

  4. $4$%

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Correct Option: A

The velocity $V$ of a body starting from rest and moving with uniform acceleration a is calculated by the formula $V = \sqrt { 2 a s }$. Here $S$ represents the displacement. If error in measurement of acceleration is 4% and error in measurement of displacement is 2%, then the error in calculation of veiocity is 

physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

  1. 2%

  2. 3%

  3. 6%

  4. 8%

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Correct Option: B
Explanation:

\begin{array}{l} According\, to\, \, question............... \ V=\sqrt { 2as }  \ error\, \, in\, \, V=\dfrac { 1 }{ 2 } \left( { error\, in\, \, acceleration\, \, +\, error\, \, in\, \, displacement } \right)  \ error\, \, in\, \, V=\frac { 1 }{ 2 } \left( { 4\, \, +\, 2 } \right)  \ \therefore \, \, \, \, error\, \, in\, \, V=\dfrac { 6 }{ 2 } =3 percent\ so\, \, the\, \, \, correct\, \, option\, \, is\, \, B. \end{array}

The current voltage relation of diode is given by $I=\left( { e }^{ 1000V/T }-1 \right)mA$, where the applied voltage $V$ is in kelvin. If a student makes an error measuring $\pm 0.01V$ while measuring the current of $5mA$ at $300k$, what will be the error in the value of current in mA?

physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

  1. $0.2mA$

  2. $0.02mA$

  3. $0.5mA$

  4. $0.05mA$

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Correct Option: C

Zero error of an instrument introduces:

physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

  1. Systematic errors

  2. Random errors

  3. Both

  4. None

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Correct Option: A
Explanation:

Random errors in experimental measurements are caused by unknown and unpredictable changes in the experiment.
Systematic errors in experimental observations usually come from the measuring instruments.
Thus zero error is recognized as the systematic error (factual).

If $f=x^2$, then the relative error in $f$ is :

physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

  1. $\dfrac {2\Delta x}{x}$

  2. $\dfrac {(\Delta x)^2}{x}$

  3. $\dfrac {\Delta x}{x}$

  4. $(\Delta x)^2$

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Correct Option: A
Explanation:

Given that: $f = x^2$
Hence, $\dfrac{df}{dx} = 2x$

Therefore: $\Delta f = \dfrac{df}{dx} \Delta x = 2x \Delta x$

The relative error in $f$ is: 
$\dfrac{\Delta f}{f} = \dfrac{2x \Delta x}{x^2}$

$\dfrac{\Delta f}{f} = \dfrac{2 \Delta x}{x}$