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Error in quantity raised to some power - (Concept)
when $\left(x=\frac{a^n}{b^m}\right)$
- The maximum fractional error in x is:- $\frac{\Delta x}{x}= \pm\left(n \frac{\Delta a}{a}+m \frac{\Delta b}{b}\right)$
- Percentage error in the value of $\mathrm{x}==\frac{\Delta x}{x} * 100= \pm\left(n \frac{\Delta a}{a} * 100+m \frac{\Delta b}{b} * 100\right)$
| Exam | Chapter |
| JEE MAIN | Physics and Measurement |
The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the percentage errors in measuring the mass and length are respectively 1.5% and 1%, the maximum percentage error in determining the density is :
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| D. |
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The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5%
respectively in the measurement of a physical quantity
The maximum percentage error in the value of A will be :
| A. |
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| C. |
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| D. |
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The relative error in the determination of the surface area of a sphere is α. Then the relative error in the determination of its volume is :
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| D. |
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The length of a cylinder is measured with a meter rod having the least count of 0.1 cm. Its diameter is measured with vernier calipers having the least count of 0.01 cm. Given that the length is 5.0 cm. and the radius is 2.0 cm. The percentage error in the calculated value of the volume will be
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| D. |
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A physical parameter a can be determined by measuring the parameters b, c, d and e using the relation . If the maximum errors in the measurement of b, c, d and e are
%,
%,
% and
%, then the maximum error in the value of a determined by the experiment is
| A. |
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| B. |
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| C. |
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| D. |
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A physical quantity P is described by the relation, P= a1/2 b2 c3 d-4. If the relative errors in the measurement of a, b, c and d, respectively, are 2%, 1%, 3% and 5%, then the percentage error in P will be :
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| D. |
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The period of oscillation of a simple pendulum is Measured in value of 'L' is 1.0 m from a meter scale having a minimum division of 1 mm and the time of one complete oscillation is 1.95 s measured from a stopwatch of 0.01s resolution. The percentage error in the determination of 'g' will be :
| A. |
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| B. |
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| D. |
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The radius of a sphere is measured to be cm. Suppose the percentage error in its volume is x:
The value of x, to the nearest integer is_______.
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In the experiment of Ohm's law, a potential difference of 5.0 V is applied across the end of a conductor of length 10.0 cm and diameter of 5.00 mm. The measured current in the conductor is 2.00 A. The maximum permissible percentage error in the resistivity of the conductor is :
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| D. |
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The time period of a simple pendulum is given by . The measured value of the length of the pendulum is 10 cm known to a 1 mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 seconds using a clock of 1 s resolution. The percentage accuracy in the determination of 'g' using this pendulum is 'x'. The value of 'x' to the nearest integer is,
| A. |
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In order to determine the Young's modulus of a wire of radius 0.2cm ( measured using a scale of least count = 0.001cm) and length 1m (measured using a scale of least count 1mm), a weight of mass 1kg (measured using a scale of least count =1g) was hanged to get elongation of 0.5cm (measured using a scale of least count 0.001cm). What will be the fractional error in the value of Young's Modulus determined by this experiment?
| A. |
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| D. |
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For , where
is a constant. If percentage error in the measurement of
and
are
and
respectively, then the percentage error for
will be ________
.
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| C. |
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| D. |
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In an experiment to find acceleration due to gravity using simple pendulum, time period of
is measured from time of 100 oscillation with a watch of
resolution. If measured value of length is
known to
accuracy, The accuracy in the determination of
is found to be
. The value of
is__________.
| A. |
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| B. |
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| C. |
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| D. |
|
A physical quantity ' $y$ ' is represented by the formula $y=m^2 r^{-4} g^x l^{-\frac{3}{2}}$
If the percentage errors found in $\mathrm{y}, \mathrm{m}, \mathrm{r}, \mathrm{I}$ and g are $18,1,0.5,4$ and p respectively, then find the value of $\mathbf{x}$ and $\mathbf{p}$.
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The acceleration due to gravity is found up to an accuracy of 4% on a planet. The energy supplied to a simple pendulum of known mass 'm' to undertake oscillations of time period T is being estimated. If time period is measured to an accuracy of 3%, the accuracy to which E is known as______%.
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A student determined Young's Modulus of elasticity using the formula .
The value of is taken to be
, without any significant error, his observations are as follows,
|
Physical Quantity |
Least count of the Equipment |
Observed Value |
| Mass (M) | ||
| Length of bar(L) | ||
| Breadth of bar(b) | ||
| Thickness of bar(d) | ||
| Depression |
Then the fractional error in the measurement of Y is :
| A. |
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| D. |
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Let where
then the value of '
' is given by :
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Joule's law of heating gives us $H=I^2 R t$ where I is current R is resistance and t is time. If the error in measurement I, R and t are 5 %, 4 % and 8 % respectively then the error in measurement of H is :
| A. |
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| D. |
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The period of oscillation of a simple pendulum is given by
, Where
is about
known with an accuracy of
. This time is about
. The time up to
oscillations is measured with a stopwatch of at least
The percentage error in g is:
| A. |
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| B. |
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| C. |
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| D. |
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A cylindrical wire of mass has length
and radius
. The maximum error in its density will be:
| A. |
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| B. |
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| C. |
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| D. |
|
A physical quantity P is given as $P=\frac{a^2 b^3}{c \sqrt{d}}$. The percentage error in the measurement of $\mathrm{a}, \mathrm{b}, \mathrm{c}$ and d are $1 \%, 2 \%, 3 \%$ and $4 \%$ respectively. The percentage error in the measurement of quantity $\mathbf{P}$ will be :
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You measure two quantities as $A=1.0 \mathrm{~m} \pm 0.2 \mathrm{~m}, B=2.0 \mathrm{~m} \pm 0.2 \mathrm{~m}$. We should report correct value for $\sqrt{ \mathrm{AB}}$ as:
| A. |
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| B. |
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| C. |
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| D. |
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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:
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| B. |
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| C. |
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| D. |
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In a simple pendulum, experiment for determination of acceleration due to gravity (g), the time taken for 40 oscillations is measured by using a watch of 2 second least count. the mean value of time taken comes out to be 60 seconds. The length of the pendulum was measured by a meter scale of least count 2 mm and the value obtained 60 cm. The percentage error in the determination of g close to _____
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| D. |
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In an experiment to measure focal length (f) of convex lens, the least counts of the measuring scales for the position of object (u) and for the position of image (v) are $\Delta u$ and $\Delta v$, respectively. The error in the measurement of the focal length of the convex lens will be :
| A. |
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| B. |
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| C. |
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| D. |
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To find the spring constant (k) of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in measurement of mass. The percentage error in determining value of k is:
| A. |
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| B. |
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| C. |
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| D. |
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The object distance and image distance are measured as $(3 \pm 0.1)_{\mathrm{cm}}$ and $(4 \pm 0.2) \mathrm{cm}$ respectively. Then the focal length of the mirror is ( use mirror formula $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$ )
| A. |
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| B. |
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| C. |
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| D. |
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The physical parameters $P, Q, R, S$ can be determined by measuring the parameters $a, b, c$ using the relations.
$\begin{aligned}
P & =a^2 b c \\
Q & =a b^2 c \\
R & =a b c^2 \\
S & =\sqrt{a b c}
\end{aligned}$
If the maximum percentage error in the measurement of $P, Q, R$ is $1^o / o, 3^o / o 4^o / o$ respectively. Then what is the maximum percentage error in measurement of $S$?
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| D. |
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The velocity relation of a bike is given by $v=\left[e^{\frac{500 \cdot D}{T}}-5\right] \mathrm{m} / \mathrm{s}$, where the v =velocity in m/s , D = displacement in 'm' and T = time in seconds. If the velocity measuring instrument made an error while measuring displacement and that error is $\pm 0.05 \mathrm{~m}$ while measuring the velocity 5m/s at 20 seconds. What will be the error in the value of velocity in m/s?
| A. |
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| B. |
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| C. |
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| D. |
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If the current through a resistor in a circuit increases by 3%, the power dissipated by the resistor
| A. |
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| B. |
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| C. |
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| D. |
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The maximum percentage error in the measurement of the density of a wire is:
[Given, mass of wire $=(0.60 \pm 0.003) \mathrm{g}$
radius of wire $=(0.50 \pm 0.01) \mathrm{cm}$
length of wire $(10.00 \pm 0.05) \mathrm{cm}]$
| A. |
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| B. |
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| C. |
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| D. |
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A tiny metallic rectangular sheet has a length and breadth of 5 mm and 2.5 mm, respectively. Using a specially designed screw gauge which has a pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be $\frac{\mathrm{x}}{100}$ where x is _________.
| A. |
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| B. |
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| C. |
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| D. |
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A quantity Q is formulated as $\mathrm{X}^{-2} \mathrm{Y}^{+\frac{3}{2}} \mathrm{Z}^{-\frac{2}{5}} \cdot \mathrm{X}, \mathrm{Y}$ and Z are independent parameters which have fractional errors of $0.1,0.2$ and 0.5 , respectively in measurement. The maximum fractional error of Q is
| A. |
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| B. |
|
| C. |
|
| D. |
|
A physical quantity C is related to four other quantities $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s as follows
$
\mathrm{C}=\frac{\mathrm{pq}^2}{\mathrm{r}^3 \sqrt{\mathrm{~s}}}
$
The percentage errors in the measurement of $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s are $1 \%, 2 \% 3 \%$ and $2 \%$ respectively.
The percentage error in the measurement of C will be _____%.
| A. |
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| B. |
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| C. |
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| D. |
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The relative error in a physical quantity raised to the power k is the k times the relative error in the individual quantity.
= absolute error in measurement of Z
= absolute error in measurement of A
= absolute error in measurement of B
= absolute error in measurement of C
p,q,r - powers over respective quantities
