List of top Physics Questions on Error analysis

Consider a series of measurements of the length of a box in an experiment. The readings are 2.4m, 2.5m, 2.6m, 2.8m, 3.0m. What would be the relative error?

The maximum percentage error in the measurement of the density of a wire is: \[ \text{Given, mass of wire} = (0.60 \pm 0.003) \, \text{g}, \quad \text{radius of wire} = (0.50 \pm 0.01) \, \text{cm}, \quad \text{length of wire} = (10.00 \pm 0.05) \, \text{cm}. \]

A physical quantity \( Q \) is related to four observables \( a \), \( b \), \( c \), and \( d \) as follows: \[ Q = \frac{a b^4}{c d^2} \] Where:
- \( a = (60 \pm 3) \, \text{Pa} \),
- \( b = (20 \pm 0.1) \, \text{m} \),
- \( c = (40 \pm 0.2) \, \text{N·s/m}^2 \),
- \( d = (50 \pm 0.1) \, \text{m} \).
Then the percentage error in \( Q \) is:

A vernier callipers has 20 divisions on the vernier scale, which coincides with 19^th division on the main scale. The least count of the instrument is 0.1 mm. One main scale division is equal to ____mm.

A physical quantity \( Q \) is found to depend on quantities \( a \), \( b \), \( c \) by the relation\[Q = \frac{a^4 b^3}{c^2}.\]The percentage errors in \( a \), \( b \), and \( c \) are 3%, 4%, and 5% respectively. Then, the percentage error in \( Q \) is:

Young's modulus is determined by the equation given by:\[ Y = \frac{49000 \, M}{\ell} \, \text{dyne/cm}^2 \] where \(M\) is the mass and \(\ell\) is the extension of the wire used in the experiment. Now, the error in Young's modulus (\(Y\)) is estimated by taking data from the \(M-\ell\) plot on graph paper. The smallest scale divisions are \(5 \, \text{g}\) and \(0.02 \, \text{cm}\) along the load axis and extension axis, respectively. If the value of \(M\) and \(\ell\) are \(500 \, \text{g}\) and \(2 \, \text{cm}\), respectively, then the percentage error of \(Y\) is:

The radius (\(r\)), length (\(l\)), and resistance (\(R\)) of a metal wire were measured in the laboratory as: \(r = (0.35 \pm 0.05) \, \text{cm}, \quad R = (100 \pm 10) \, \text{ohm}, \quad l = (15 \pm 0.2) \, \text{cm}.\)
The percentage error in the resistivity of the material of the wire is:

In an experiment to measure focal length (\(f\)) of a convex lens, the least counts of the measuring scales for the position of the object (\(u\)) and for the position of the image (\(v\)) are \( \Delta u \) and \( \Delta v \), respectively. The error in the measurement of the focal length of the convex lens will be: