IB Physics Uncertainties

A tutorial sheet on sub topic 1.2 is given below.

1. The mass of a pencil is measured once. The value is 4g. What is the uncertainty in this measurement?
2. A ball is released from rest and the time to fall a fixed distance is measured. The times are 0.5s, 0.5s, 0.6s and 0.6s. What is the uncertainty in the time of fall?
3. A student measures the following value for g in ms-2: 9.81, 9.79, 9.84, 9.81, 9.75, 9.79, 9.83. Give the scientific value of g including its uncertainty. [9.80 ± 0.01 ms-2]
4. A toy car moves in a straight line along a horizontal laboratory bench. The time taken to move a distance of 350cm is measured 5 times. The values are 6.2s, 6.5s, 6.4s, 6.3s and 6.0s. What is the average speed of the car?
5. In the previous question the distance is measured 5 times. The values are 340cm, 360cm, 345cm, 365cm, 355 cm. Using the previous time values, what is the average speed of the car?
6. The mass of a marble is measured five times. The values are 52g, 51g, 52g, 53g, 52g. The diameter is measured five times. The values are 35mm, 33mm, 36mm, 34mm and 35mm. Determine the density of the marble.
7. A uniform rod can oscillate freely about a horizontal axis through its end point. The time of small oscillations about its equilibrium position is given by T = 2𝜋√[I/(mgh)], where m is the mass of the rod, g the acceleration due to gravity, h the distance from the point of support to the centre of the rod and I is the moment of inertia of the rod about its point of support. The following data sets are obtained for the measurement of m, h and I respectively; {210g, 208g, 209g, 211g, 212g}, {0.50m, 0.49m, 0.51m, 0.48m, 0.49m}, {0.42kgm2, 0.40kgm2, 0.46kgm2, 0.50kgm2, 0.50kgm2}. Determine g from this data.
8. The radius of a circle is 14.6±0.5cm. Determine the area of the circle to the correct number of significant figures. [(6.70±0.46)×102 cm2]
9. What is the circumference of the circle in the previous question? [91.7±3.1cm]
10. If R=1800±36Ω and I=2.1±0.1mA, what is the value of RI? [3.8±0.3V]
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