Two resistors of resistances $R_1 = (300 \pm 3) \,\Omega $ and $R_2 = (500 \pm 4)$ are connected in series. The equivalent resistance of the series combination is
Two resistors of resistances $R_1 = (300 \pm 3) \,\Omega $ and $R_2 = (500 \pm 4)$ are connected in series. The equivalent resistance of the series combination is
- A
$(800 \pm 1) \,\Omega $
- B
$(800 \pm 7) \,\Omega $
- C
$(200 \pm 7) \,\Omega $
- D
$(200 \pm 1) \,\Omega $
Similar Questions
In an experiment to determine the acceleration due to gravity $g$, the formula used for the time period of a periodic motion is $T=2 \pi \sqrt{\frac{7(R-r)}{5 g}}$. The values of $R$ and $r$ are measured to be $(60 \pm 1) \mathrm{mm}$ and $(10 \pm 1) \mathrm{mm}$, respectively. In five successive measurements, the time period is found to be $0.52 \mathrm{~s}, 0.56 \mathrm{~s}, 0.57 \mathrm{~s}, 0.54 \mathrm{~s}$ and $0.59 \mathrm{~s}$. The least count of the watch used for the measurement of time period is $0.01 \mathrm{~s}$. Which of the following statement($s$) is(are) true?
($A$) The error in the measurement of $r$ is $10 \%$
($B$) The error in the measurement of $T$ is $3.57 \%$
($C$) The error in the measurement of $T$ is $2 \%$
($D$) The error in the determined value of $g$ is $11 \%$
In an experiment to determine the acceleration due to gravity $g$, the formula used for the time period of a periodic motion is $T=2 \pi \sqrt{\frac{7(R-r)}{5 g}}$. The values of $R$ and $r$ are measured to be $(60 \pm 1) \mathrm{mm}$ and $(10 \pm 1) \mathrm{mm}$, respectively. In five successive measurements, the time period is found to be $0.52 \mathrm{~s}, 0.56 \mathrm{~s}, 0.57 \mathrm{~s}, 0.54 \mathrm{~s}$ and $0.59 \mathrm{~s}$. The least count of the watch used for the measurement of time period is $0.01 \mathrm{~s}$. Which of the following statement($s$) is(are) true?
($A$) The error in the measurement of $r$ is $10 \%$
($B$) The error in the measurement of $T$ is $3.57 \%$
($C$) The error in the measurement of $T$ is $2 \%$
($D$) The error in the determined value of $g$ is $11 \%$
- [IIT 2016]
The length of a cylinder is measured with a metre rod having least count $0.1 \;cm$. Its diameter is measured with vernier calipers having least count $0.01\; cm$. If the length and diameter of the cylinder are $5.0\; cm$ and $2.00\; cm$, respectively, then the percentage error in the calculated value of volume will be
The length of a cylinder is measured with a metre rod having least count $0.1 \;cm$. Its diameter is measured with vernier calipers having least count $0.01\; cm$. If the length and diameter of the cylinder are $5.0\; cm$ and $2.00\; cm$, respectively, then the percentage error in the calculated value of volume will be
The maximum percentage errors in the measurement of mass (M), radius (R) and angular velocity $(\omega)$ of a ring are $2 \%, 1 \%$ and $1 \%$ respectively, then find the maximum percenta? error in the measurement of its moment of inertia $\left(I=\frac{1}{2} M R^{2}\right)$ about its geometric axis.
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A students measures the distance traversed in free fall of a body, the initially at rest, in a given time. He uses this data to estimate $g$ , the acceleration due to gravity . If the maximum percentage errors in measurement of the distance and the time are $e_1$ and $e_2$ respectively, the percentage error in the estimation of $g$ is
A students measures the distance traversed in free fall of a body, the initially at rest, in a given time. He uses this data to estimate $g$ , the acceleration due to gravity . If the maximum percentage errors in measurement of the distance and the time are $e_1$ and $e_2$ respectively, the percentage error in the estimation of $g$ is
- [AIPMT 2010]
The amount of heat produced in an electric circuit depends upon the current $(I),$ resistance $(R)$ and time $(t).$ If the error made in the measurements of the above quantities are $2\%, 1\%$ and $1\%$ respectively then the maximum possible error in the total heat produced will be ........... $\%$
The amount of heat produced in an electric circuit depends upon the current $(I),$ resistance $(R)$ and time $(t).$ If the error made in the measurements of the above quantities are $2\%, 1\%$ and $1\%$ respectively then the maximum possible error in the total heat produced will be ........... $\%$
- [AIEEE 2012]