The acceleration due to gravity is measured on the surface of earth by using a simple pendulum. If $\alpha$ and $\beta$ are relative errors in the measurement of length and time period respectively, then percentage error in the measurement of acceleration due to gravity is
The acceleration due to gravity is measured on the surface of earth by using a simple pendulum. If $\alpha$ and $\beta$ are relative errors in the measurement of length and time period respectively, then percentage error in the measurement of acceleration due to gravity is
- A
$\left(\alpha+\frac{1}{2} \beta\right) \times 100$
- B
$(\alpha-2 \beta)$
- C
$(2 \alpha+\beta) \times 100$
- D
$(\alpha+2 \beta) \times 100$
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- [JEE MAIN 2021]
$Assertion$ : The error in the measurement of radius of the sphere is $0.3\%$. The permissible error in its surface area is $0.6\%$
$Reason$ : The permissible error is calculated by the formula $\frac{{\Delta A}}{A} = \frac{{4\Delta r}}{r}$
$Assertion$ : The error in the measurement of radius of the sphere is $0.3\%$. The permissible error in its surface area is $0.6\%$
$Reason$ : The permissible error is calculated by the formula $\frac{{\Delta A}}{A} = \frac{{4\Delta r}}{r}$
- [AIIMS 2008]
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In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is $10 \pm 0.1 \mathrm{~cm}$ and the distance of its real image from the lens is $20 \pm 0.2 \mathrm{~cm}$. The error in the determination of focal length of the lens is $n \%$. The value of $n$ is. . . . . . .
- [IIT 2023]