The random error in the arithmetic mean of $100$ observations is $x$; then random error in the arithmetic mean of $400$ observations would be
The random error in the arithmetic mean of $100$ observations is $x$; then random error in the arithmetic mean of $400$ observations would be
- A
$4x$
- B
$\frac{1}{4}x$
- C
$2x$
- D
$\frac{1}{2}x$
Similar Questions
A physical quantity is $A = P^2/Q^3.$ The percentage error in measurement of $P$ and $Q$ is $x$ and $y$ respectively. Maximum error in measurement of $A$ is
A physical quantity is $A = P^2/Q^3.$ The percentage error in measurement of $P$ and $Q$ is $x$ and $y$ respectively. Maximum error in measurement of $A$ is
The initial and final temperatures of water as recorded by an observer are $(40.6 \pm 0.2)^{\circ} C$ and $(78.9 \pm 0.3)^{\circ} C .$ Calculate the rise in temperature with proper error limits.
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In a simple pendulum experiment for determination of acceleration due to gravity $(g)$, 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 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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- [JEE MAIN 2019]
A student determined Young's Modulus of elasticity using the formula $Y=\frac{M g L^{3}}{4 b d^{3} \delta} .$ The value of $g$ is taken to be $9.8 \,{m} / {s}^{2}$, without any significant error, his observation are as following.
Physical Quantity
Least count of the Equipment used for measurement
Observed value
Mass $({M})$
$1\; {g}$
$2\; {kg}$
Length of bar $(L)$
$1\; {mm}$
$1 \;{m}$
Breadth of bar $(b)$
$0.1\; {mm}$
$4\; {cm}$
Thickness of bar $(d)$
$0.01\; {mm}$
$0.4 \;{cm}$
Depression $(\delta)$
$0.01\; {mm}$
$5 \;{mm}$
Then the fractional error in the measurement of ${Y}$ is
A student determined Young's Modulus of elasticity using the formula $Y=\frac{M g L^{3}}{4 b d^{3} \delta} .$ The value of $g$ is taken to be $9.8 \,{m} / {s}^{2}$, without any significant error, his observation are as following.
| Physical Quantity | Least count of the Equipment used for measurement | Observed value |
| Mass $({M})$ | $1\; {g}$ | $2\; {kg}$ |
| Length of bar $(L)$ | $1\; {mm}$ | $1 \;{m}$ |
| Breadth of bar $(b)$ | $0.1\; {mm}$ | $4\; {cm}$ |
| Thickness of bar $(d)$ | $0.01\; {mm}$ | $0.4 \;{cm}$ |
| Depression $(\delta)$ | $0.01\; {mm}$ | $5 \;{mm}$ |
Then the fractional error in the measurement of ${Y}$ is
- [JEE MAIN 2021]
Find the relative error in $Z,$ if $Z=\frac{A^{4} B^{1 / 3}}{ C D^{3 / 2}}$
Find the relative error in $Z,$ if $Z=\frac{A^{4} B^{1 / 3}}{ C D^{3 / 2}}$