A physical quantity $X$ is given by $X = \frac{{2{k^3}{l^2}}}{{m\sqrt n }}$ The percentage error in the measurements of $k,\,l,\, m$ and $n$ are $1\%, 2\%, 3\%$ and $4\%$ respectively. The value of $X$ is uncertain by .......... $\%$
A physical quantity $X$ is given by $X = \frac{{2{k^3}{l^2}}}{{m\sqrt n }}$ The percentage error in the measurements of $k,\,l,\, m$ and $n$ are $1\%, 2\%, 3\%$ and $4\%$ respectively. The value of $X$ is uncertain by .......... $\%$
- A
$8$
- B
$10$
- C
$12$
- D
$14$
Similar Questions
The mass of the body is $10.000\,g$ and its volume is $10.00\,cm^3$. If the measured values are expressed upto the correct significant figures, the maximum error in the measurement of density is
The mass of the body is $10.000\,g$ and its volume is $10.00\,cm^3$. If the measured values are expressed upto the correct significant figures, the maximum error in the measurement of density is
The resistance $\mathrm{R}=\frac{\mathrm{V}}{\mathrm{I}}$ where $\mathrm{V}=(200 \pm 5) \mathrm{V}$ and $I=(20 \pm 0.2) A$, the percentage error in the measurement of $R$ is :
The resistance $\mathrm{R}=\frac{\mathrm{V}}{\mathrm{I}}$ where $\mathrm{V}=(200 \pm 5) \mathrm{V}$ and $I=(20 \pm 0.2) A$, the percentage error in the measurement of $R$ is :
- [JEE MAIN 2024]
The length and width of a rectangular room are measured to be $3.95 \pm 0.05 \,m$ and $3.05 \pm 0.05 \,m$, respectively. The area of the floor is .................... $m^2$
- [KVPY 2016]
A student uses a simple pendulum of exactly $1 \mathrm{~m}$ length to determine $\mathrm{g}$, the acceleration due to gravity. He uses a stop watch with the least count of $1 \mathrm{sec}$ for this and records $40$ seconds for $20$ oscillations. For this observation, which of the following statement$(s)$ is (are) true?
$(A)$ Error $\Delta T$ in measuring $T$, the time period, is $0.05$ seconds
$(B)$ Error $\Delta \mathrm{T}$ in measuring $\mathrm{T}$, the time period, is $1$ second
$(C)$ Percentage error in the determination of $g$ is $5 \%$
$(D)$ Percentage error in the determination of $g$ is $2.5 \%$
A student uses a simple pendulum of exactly $1 \mathrm{~m}$ length to determine $\mathrm{g}$, the acceleration due to gravity. He uses a stop watch with the least count of $1 \mathrm{sec}$ for this and records $40$ seconds for $20$ oscillations. For this observation, which of the following statement$(s)$ is (are) true?
$(A)$ Error $\Delta T$ in measuring $T$, the time period, is $0.05$ seconds
$(B)$ Error $\Delta \mathrm{T}$ in measuring $\mathrm{T}$, the time period, is $1$ second
$(C)$ Percentage error in the determination of $g$ is $5 \%$
$(D)$ Percentage error in the determination of $g$ is $2.5 \%$
- [IIT 2010]
Error in volume of a sphere is $6\%$. Error in its radius will be .......... $\%$
Error in volume of a sphere is $6\%$. Error in its radius will be .......... $\%$