Errors in Measurement

Unspecified year 28 questions

1. Systematic errors can be
2. Random error can be eliminated by
3. The is the error associated with the resolution of the instrument.
4. The smallest value that can be measured by the measuring instrument is called
5. Which of the following is not a systematic error?
6. A torque meter is calibrated to reference standards of mass, length and time each with 5% accuracy. After calibration, the measured torque with this torque meter will have net accuracy of:
7. A simple pendulum is being used to determine the value of gravitational acceleration at a certain place. The length of the pendulum is 25.0cm and a stop watch with 1s resolution measures the time taken for 40 oscillations to be 50s. The accuracy in g is
8. A physical quantity z depends on four observables a, b, c and d, as $z = (a^{2}b^{2/3})/(\sqrt{c} d^{3})$. The percentages of error in the measurement of a, b, c and d are 2%, 1.5%, 4% and 2.5% respectively. The percentage of error in z is:
9. If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is:
10. The magnitude of the difference between the individual measurement and true value of the quantity is called
11. When two quantities are divided, the relative error in the result is given by
12. Two masses $M_{A}$ and $M_{B} (M_{A} < M_{B})$ are weighed using same weighing machine. Absolute error and relative error in two measurement are (Assume only systematic errors are involved)
13. The refractive index of water measured by the relation $\mu$ = (real depth)/(apparent depth) is found to have values of 1.34, 1.38, 1.32 and 1.36; the mean value of refractive index with percentage error is
14. If $Z = A^{3}$, then $\Delta Z/Z$ =
15. Error in the measurement of radius of a sphere is 1%. Then error in the measurement of volume is
16. Resistance $R = V/h$, here $V = (100 \pm 5)V$ and $I = (100 \pm 0.2) A$. Find percentage error in R.
17. If $x = a - b$, then the maximum percentage error in the measurement of x will be
18. A wire has a mass $0.3 \pm 0.003g$, radius $0.5 \pm 0.005mm$ and length $6 \pm 0.06cm$. The maximum percentage error in the measurement of its density is
19. Find equivalent resistance when $R_{1} = (100 \pm 3)\Omega$ and $R_{2} = (200 \pm 4)\Omega$ when connected in series
20. If $Z = A^{4}B^{1/3}/CD^{3/2}$, than relative error in Z. $\Delta Z/Z$ is equal to
21. Relative density of a metal may be found with the help of spring balance. In air the spring balance reads $(5.00 \pm 0.05)N$ and in water it reads $(4.00 \pm 0.05)N$. Then, the relative density along with the maximum permissible percentage error would be
22. A quantity is represented by $X = M^{a}L^{b}T^{c}$. The % error in measurement of M, L and T are a%, b% and g% respectively. The % error in X would be
23. In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows $P = (a^{3}b^{2})/(cd)$ % error in P is
24. The heat generated in a circuit is given by $Q = I^{2}Rt$, where I is current, R is resistance and t is time. If the percentage errors in measuring I, R and t are 2%, 1% and 1% respectively, then the maximum error in measuring heat will be
25. A physical quantity P is described by the relation $P = a^{1/2}b^{2}c^{3}d^{-4}$. If the relative errors in the measurement of a, b, c and d respectively, are 2%, 1%, 3% and 5%, then the relative error in P will be:
26. The pressure on a square plate is measured by measuring the force on the plate and length of the sides of the plate by using the formula $P = F/\ell^{2}$. If the maximum errors in the measurement of force and length are 6% and 3% respectively, then the maximum error in the measurement of pressure is
27. A physical quantity $\zeta$ is calulated using the formula $\zeta = (1/10)xy^{2}/z^{1/3}$, where x, y and z are experimentally measured quantities. If the fractional error in the measurement of x, y and z are 2%, 1% and 3% respectively, then the percentage error in $\zeta$ will be
28. In a simple pendulum experiment, the maximum percentage error in the measurement of length is 2% and that in the observation of the time-period is 3%. Then the maximum percentage error in determination of the acceleration due to gravity g is