The density of a cube is measured by measuring its mass and the length of its sides. If the maximum error in the measurement of mass and length are $3\%$ and $2\%$ respectively, then find the maximum error in the measurement of the density of cube.......... $\%$
The density of a cube is measured by measuring its mass and the length of its sides. If the maximum error in the measurement of mass and length are $3\%$ and $2\%$ respectively, then find the maximum error in the measurement of the density of cube.......... $\%$
- [AIPMT 1996]
- A
$12$
- B
$14$
- C
$7$
- D
$9$
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- [AIPMT 1995]
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]
Two resistance are measured in $Ohm$ and is given as
$R_1 = 3 \Omega \pm 1\%$ and $R_2 = 6 \Omega \pm 2\%$ When they are connected in parallel, the percentage error in equivalent resistance is.......... $\%$
Two resistance are measured in $Ohm$ and is given as
$R_1 = 3 \Omega \pm 1\%$ and $R_2 = 6 \Omega \pm 2\%$ When they are connected in parallel, the percentage error in equivalent resistance is.......... $\%$
An experiment measures quantities $a, b$ and $c$, and quantity $X$ is calculated from $X=a b^{2} / c^{3}$. If the percentage error in $a$, $b$ and $c$ are $\pm 1 \%, \pm 3 \%$ and $\pm 2 \%$, respectively, then the percentage error in $X$ will be
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