The percentage error in measurement of a physical quantity $m$ given by $m = \pi \tan \theta $ is minimum when $\theta $ $=$ .......... $^o$ (Assume that error in $\theta $ remain constant)
The percentage error in measurement of a physical quantity $m$ given by $m = \pi \tan \theta $ is minimum when $\theta $ $=$ .......... $^o$ (Assume that error in $\theta $ remain constant)
- A
$45$
- B
$90$
- C
$60$
- D
$30$
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]
Explain Absolute Error, Relative Error and Percentage Error.
Explain Absolute Error, Relative Error and Percentage Error.
A packet contains silver powder of mass $20.23 \,g \pm 0.01 \,g$. Some of the powder of mass $5.75 \,g \pm 0.01 \,g$ is taken out from it. The mass of the powder left back is ................
A packet contains silver powder of mass $20.23 \,g \pm 0.01 \,g$. Some of the powder of mass $5.75 \,g \pm 0.01 \,g$ is taken out from it. The mass of the powder left back is ................
A physical quantity $p$ is described by the relation $p\, = a^{1/2}\, b^2\, c^3\, d^{-4}$
If the relative errors in the measurement of $a, b, c$ and $d$ respectively, are $2\% , 1\%, 3\%$ and $5\%$, then the relative error in $P$ will be ........... $\%$
A physical quantity $p$ is described by the relation $p\, = a^{1/2}\, b^2\, c^3\, d^{-4}$
If the relative errors in the measurement of $a, b, c$ and $d$ respectively, are $2\% , 1\%, 3\%$ and $5\%$, then the relative error in $P$ will be ........... $\%$
- [JEE MAIN 2017]
A physical quantity $z$ depends on four observables $a,$ $b,$ $c$ and $d ,$ as $z =\frac{ a ^{2} b ^{\frac{2}{3}}}{\sqrt{ c } d ^{3}} .$ The percentage of error in the measurement of $a, b, c$ and $d$ are $2 \%, 1.5 \%, 4 \%$ and $2.5 \%$ respectively. The percentage of error in $z$ is$......\%$
A physical quantity $z$ depends on four observables $a,$ $b,$ $c$ and $d ,$ as $z =\frac{ a ^{2} b ^{\frac{2}{3}}}{\sqrt{ c } d ^{3}} .$ The percentage of error in the measurement of $a, b, c$ and $d$ are $2 \%, 1.5 \%, 4 \%$ and $2.5 \%$ respectively. The percentage of error in $z$ is$......\%$
- [JEE MAIN 2020]