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Propagation of errors (Assignment)

Q1. In an experiment the values of two resistances are measured to be R1 = 15 ± 0.2 ohm; R2 = 10 ± 0.1 ohm. Find the value of total resistance in series combination with limits of possible error. Q2. The external and internal diameters of a hollow cylinder are determined and the results are recorded as (4.23±0.01) cm and (3.9±0.01) cm. Determine the thickness of the cylinder wall with limits of error. Q3. The percentage error in the measurement of mass and speed are 3% and 2% respectively. What will be the error in the measurement of kinetic energy and momentum? Q4.The radius of a sphere is measured to be 5.3 ± 0.1 cm. Calculate the percentage error in volume. Q5. The percentage error in determining the area of a rectangular plate is 2%. If the error in the measurement of length is 1.2% what is the percentage error in the breadth? Q6. A physical quantity Z is calculated from the following relation: . If the percentage error in measuring A, B, C and D are 1%, 3%, 2% and 4% respectively, then find the percentage of error in Z. Q7. The length and breadth of a rectangular lamina are measured to be (2.3±0.2) cm and (1.6±0.1) cm. Calculate the area and perimeter with error limits? Q8. The time period of oscillations of a sample pendulum is (a) In finding the value of g, which quantity should be measured more accurately and why? (b) L is about 10 cm and is known to 1 mm accuracy. The time period of oscillation is about 0.5s. The time of 100 oscillations is measured with a wrist watch of 1 s resolution. What is the accuracy in the determination of g? Q9. To study the flow of a liquid through a narrow tube, the following formula is used . The value of p, r, V and L are 78 cm of Hg, 0.28 cm, 1.2 cm3 /s and 18.2 cm respectively. These quantities are measured to the accuracies of 0.5 cm of Hg, 0.01 cm, 0.1 cm3 /s and 0.1 cm respectively. Find the percentage error in determining the value of ƞ. Q10. The centripetal force is given by . The mass ‘m’, velocity ‘v’ an radius ‘r’ of the circular path of an object are 0.5 kg, 10 ms-1 and 0.4m respectively. If ‘m’, ‘v’ and ‘r’ are measured to the accuracy of 0.05kg, 0.01 ms-1 and 0.01m, find the percentage error in the force acting on the body. #PropagationOfErrors #Assignment #Physics #AKYSir