The length, breadth and thickness of a strip are $(10.0 \pm 0.1)\; cm ,(1.00 \pm 0.01) \;cm$ and $(0.100 \pm 0.001)\; cm$ respectively. The most probable error in its volume will be?
The length, breadth and thickness of a strip are $(10.0 \pm 0.1)\; cm ,(1.00 \pm 0.01) \;cm$ and $(0.100 \pm 0.001)\; cm$ respectively. The most probable error in its volume will be?
- A
$\pm \,0.03\, cm^{3}$
- B
$\pm\, 0.111 \,cm^{3}$
- C
$\pm\, 0.012\, cm^{3}$
- D
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Similar Questions
Three students $S_{1}, S_{2}$ and $S_{3}$ 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.
Student No.
Length of pendulum $(cm)$
No. of oscillations $(n)$
Total time for oscillations
Time period $(s)$
$1.$
$64.0$
$8$
$128.0$
$16.0$
$2.$
$64.0$
$4$
$64.0$
$16.0$
$3.$
$20.0$
$4$
$36.0$
$9.0$
(Least count of length $=0.1 \,{m}$, least count for time $=0.1\, {s}$ )
If $E_{1}, E_{2}$ and $E_{3}$ are the percentage errors in $'g'$ for students $1,2$ and $3$ respectively, then the minimum percentage error is obtained by student no. ....... .
Three students $S_{1}, S_{2}$ and $S_{3}$ 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.
| Student No. | Length of pendulum $(cm)$ | No. of oscillations $(n)$ | Total time for oscillations | Time period $(s)$ |
| $1.$ | $64.0$ | $8$ | $128.0$ | $16.0$ |
| $2.$ | $64.0$ | $4$ | $64.0$ | $16.0$ |
| $3.$ | $20.0$ | $4$ | $36.0$ | $9.0$ |
(Least count of length $=0.1 \,{m}$, least count for time $=0.1\, {s}$ )
If $E_{1}, E_{2}$ and $E_{3}$ are the percentage errors in $'g'$ for students $1,2$ and $3$ respectively, then the minimum percentage error is obtained by student no. ....... .
- [JEE MAIN 2021]
A physical quantity $X$ is related to four measurable quantities $a,\, b,\, c$ and $d$ as follows $X = a^2b^3c^{\frac {5}{2}}d^{-2}$. The percentange error in the measurement of $a,\, b,\, c$ and $d$ are $1\,\%$, $2\,\%$, $3\,\%$ and $4\,\%$ respectively. What is the percentage error in quantity $X$ ? If the value of $X$ calculated on the basis of the above relation is $2.763$, to what value should you round off the result.
A physical quantity $X$ is related to four measurable quantities $a,\, b,\, c$ and $d$ as follows $X = a^2b^3c^{\frac {5}{2}}d^{-2}$. The percentange error in the measurement of $a,\, b,\, c$ and $d$ are $1\,\%$, $2\,\%$, $3\,\%$ and $4\,\%$ respectively. What is the percentage error in quantity $X$ ? If the value of $X$ calculated on the basis of the above relation is $2.763$, to what value should you round off the result.
According to Joule's law of heating, heat produced $H = {I^2}\,Rt$, where I is current, $R$ is resistance and $t$ is time. If the errors in the measurement of $I, R$ and t are $3\%, 4\% $ and $6\% $ respectively then error in the measurement of $H$ is
According to Joule's law of heating, heat produced $H = {I^2}\,Rt$, where I is current, $R$ is resistance and $t$ is time. If the errors in the measurement of $I, R$ and t are $3\%, 4\% $ and $6\% $ respectively then error in the measurement of $H$ is
In an experiment of determine the Young's modulus of wire of a length exactly $1\; m$, the extension in the length of the wire is measured as $0.4\,mm$ with an uncertainty of $\pm 0.02\,mm$ when a load of $1\,kg$ is applied. The diameter of the wire is measured as $0.4\,mm$ with an uncertainty of $\pm 0.01\,mm$. The error in the measurement of Young's modulus $(\Delta Y)$ is found to be $x \times 10^{10}\,Nm ^{-2}$. The value of $x$ is
$\left[\right.$ Take $\left.g =10\,m / s ^{2}\right]$
In an experiment of determine the Young's modulus of wire of a length exactly $1\; m$, the extension in the length of the wire is measured as $0.4\,mm$ with an uncertainty of $\pm 0.02\,mm$ when a load of $1\,kg$ is applied. The diameter of the wire is measured as $0.4\,mm$ with an uncertainty of $\pm 0.01\,mm$. The error in the measurement of Young's modulus $(\Delta Y)$ is found to be $x \times 10^{10}\,Nm ^{-2}$. The value of $x$ is
$\left[\right.$ Take $\left.g =10\,m / s ^{2}\right]$
- [JEE MAIN 2022]
The length of a uniform rod is $100.0 \,cm$ and radius is $1.00 \,cm$. If length is measured with a meter rod having least count $1 \,mm$ and radius is measured with vernier callipers having least count $0.1 \,mm$, the percentage error in calculated volume of cylinder is ............. $\%$
The length of a uniform rod is $100.0 \,cm$ and radius is $1.00 \,cm$. If length is measured with a meter rod having least count $1 \,mm$ and radius is measured with vernier callipers having least count $0.1 \,mm$, the percentage error in calculated volume of cylinder is ............. $\%$