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Error in product and Error in division of two physical quantities - (Concept)
1) Error in product $x=a b$
- maximum fractional error $=\frac{\Delta x}{x}= \pm\left(\frac{\Delta a}{a}+\frac{\Delta b}{b}\right)$
where
$\Delta a=$ absolute error in measurement of a
$\Delta b=$ absolute error in measurement of b
$\Delta x=$ absolute error in measurement of x
- The percentage error in the value of $\mathrm{x}=\frac{\Delta x}{x} * 100= \pm\left(\frac{\Delta a}{a} * 100+\frac{\Delta b}{b} * 100\right)$
$=(\%$ error in value of $a+\%$ error in value of b)
2) Error in division $x=\frac{a}{b}$
- maximum fractional error in $\mathrm{x}=\frac{\Delta x}{x}= \pm\left(\frac{\Delta a}{a}+\frac{\Delta b}{b}\right)$
- The percentage error in the value of $\mathrm{x}=\frac{\Delta x}{x} * 100= \pm\left(\frac{\Delta a}{a} * 100+\frac{\Delta b}{b} * 100\right)$
$=(\%$ error in value of $a+\%$ error in value of b)
| Exam | Chapter |
| JEE MAIN | Physics and Measurement |
A physical quantity P depends on the other two physical quantities Q and R, as follows P = Where a is constant. In an experiment, the quantity Q is determined by measuring P and R and using the above expression. If the percentage of error in the measurement of P and R is 10 % and 12 % respectively, Then the percentage of error in determining the value of Q is :
| A. |
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| B. |
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| C. |
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| D. |
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The resistance R = V / I where V = 100 4 volts and I = 10
0.3 ampere. What is the maximum percentage error in R
| A. |
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| B. |
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| C. |
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| D. |
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In the density measurement of a cube, the mass and edge length are measured as $(10.00 \pm 0.10) \mathrm{kg}_{\text {and }}$ $(0.10 \pm 0.01) \mathrm{m}$, respectively. The relative error in the measurement of density is :
| A. |
|
| B. |
|
| C. |
|
| D. |
|
If percentage error in the measurement of resistance R is 5% and that of in a measurement of current I is 2%, then the maximum percentage error in voltage V will be :
| A. |
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| B. |
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| C. |
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| D. |
|
The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is . If the relative errors in measuring the mass and diameter are 6% and 1.5 % respectively. The value of 'x' is
| A. |
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| B. |
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| C. |
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| D. |
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A physical quantity depends on four observables
and
as
. The percentages of error in the measurement of
and
are
,
,
and
respectively. The percentage of error in
is :
| A. |
|
| B. |
|
| C. |
|
| D. |
|
A silver wire has a mass , radius
and length
. The maximum percentage error in the measurement of its density will be :
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The maximum error in the measurement of resistance, current, and time for which current flows in an electrical circuit are $1 \%, 2 \%$ and $3 \%$, respectively. The maximum percentage error in the detection of the dissipated heat will be:
| A. |
|
| B. |
|
| C. |
|
| D. |
|
A torque meter is calibrated to reference standards of mass, length and time each with accuracy. After calibration, the measured torque with this torque meter will have a net accuracy of:
| A. |
|
| B. |
|
| C. |
|
| D. |
|
Three students perform an experiment for determining the acceleration due to gravity (g) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table.
(Least count of length , least count for time
)
If If $E_1, E_2$ and $E_3$ are the percentage errors in for students 1,2 and 3 respectively, then the minimum percentage error is obtained by the student no.__________.
| A. |
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| B. |
|
| C. |
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| D. |
|
In a simple pendulum experiment for the determination of acceleration due to gravity (g), the time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be 30 s. The length of the pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm. The percentage error in the determination of g is close to:
| A. |
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| B. |
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| C. |
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| D. |
|
A physical quantity $Q$ is found to depend on quantities $a, b, c$ by the relation $Q=\frac{a^4 b^3}{c^2}$. The percentage error in a, b and c are 3%,4% and 5 % respectively. Then, the percentage error in Q is:
| A. |
|
| B. |
|
| C. |
|
| D. |
|
Two roads of length $(3.161 \pm 0.3) \mathrm{cm}$ and $(1.121 \pm 0.1) \mathrm{cm}$. What is the percentage error in the measurement of their difference :
| A. |
|
| B. |
|
| C. |
|
| D. |
|
A cylindrical wire of mass $(0.4 \pm 0.01) g$ has length $(8 \pm 0.04) \mathrm{cm}$ and radius $(6 \pm 0.03) \mathrm{mm}$. The maximum error in its density will be:
| A. |
|
| B. |
|
| C. |
|
| D. |
|
If dimensions of A and B are different, then which of the following operation is valid
| A. |
|
| B. |
|
| C. |
|
| D. |
|
What is the fractional error in g calculated from $T=2 \pi \sqrt{\frac{l}{g}}$ ? Given the fractional error in T and I are $\pm \mathrm{x}$ and $\pm$ y respectively.
| A. |
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| B. |
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| C. |
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| D. |
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A physical quantity Q is measured using the formula $Q=\sqrt{\frac{X-Y}{Z}}$. The values of X and Y are measured to be $(50 \pm 1)$ and $(20 \pm 1)$ respectively. The values of measurement of $Q$ in five trials were found to be $0.52,0.56,0.57,0.53,0.59$. So the error in the measurement of $\mathrm{Q}, \mathrm{X}, \mathrm{Y}, \mathrm{Z}$ is $\mathrm{a} \%, \mathrm{~b} \%, \mathrm{c} \%$ and $\mathrm{d} \%$ respectively. The value of $(a+b+c+d)$ is:
| A. |
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| B. |
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| C. |
|
| D. |
|
In terms of $\mathrm{Q}, \mathrm{R}, \mathrm{S}$ the physical quantity P is given as $P=a Q^3 R^{-2} S^{\frac{1}{2}}$ where 'a' is constant. If percentage error in measurement of P and R and S is $10 \%, 8 \%$ and $2 \%$ respectively. Then the percentage of error in determining the value of $Q$ is:
| A. |
|
| B. |
|
| C. |
|
| D. |
|
In the ammeter-voltmeter method of measuring resistance, the error in reading of current and voltage is 1.5% and 3% respectively. The error (in %) in the measurement of resistance is
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The current-voltage relation of a diode is the relation of the diode given by I = (e1000V/T -1) mA, where the applied voltage V is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring 
V while measuring the current of 5 mA at 300 K,what will be the error in the value of current in mA ?
| A. |
|
| B. |
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| C. |
|
| D. |
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When two quantities are multiplied or divided, the relative error in the result is the sum of the relative errors in the multipliers.
= absolute error in measurement of Z
= absolute error in measurement of A
= absolute error in measurement of B
