List of top Physics Questions on Error Propagation

In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10 V and 5 A, respectively. The least counts of voltmeter and ammeter are 500 mV and 200 mA, respectively. The estimated error in the resistance measurement is :
The percentage error in the calculated volume of a sphere, if there is \(2%\) error in its diameter measurement, is _____.
The diameter of a wire measured by a screw gauge of least count \(0.001\) cm is \(0.08\) cm. The length measured by a scale of least count \(0.1\) cm is \(150\) cm. When a weight of \(100\) N is applied to the wire, the extension in length is \(0.5\) cm measured by a micrometer of least count \(0.001\) cm. The error in the measured Young’s modulus is \(\alpha \times 10^9\) N/m\(^2\). The value of \(\alpha\) is:
In a single slit diffraction experiment, a slit of width $(0.016 \pm 0.002)$ mm is used to measure the wavelength of a monochromatic light source. In the diffraction pattern, the angular distance between the central maximum and first minimum is measured to be $(2^\circ \pm 40')$. The value of the fractional error in the measurement of wavelength is:
(Given: $\sin(2^\circ) = 0.035$)
A quantity $ Q $ is formulated as $ Q = X^{-2} Y^{3/2} Z^{-2/5} $. $ X $, $ Y $, and $ Z $ are independent parameters which have fractional errors of 0.1, 0.2, and 0.5, respectively in measurement. The maximum fractional error of $ Q $ is:
The energy of a system is given as \( E(t) = \alpha e^{-\beta t \), where \( t \) is the time and \( \beta = 0.3 \, \text{s}^{-1} \). The errors in the measurement of \( \alpha \) and \( t \) are 1.2 percent and 1.6 percent, respectively. At \( t = 5 \) s, the maximum percentage error in the energy is:}