5. Assessment Of Total Uncertainty In The Final Result: For the uncertainty in a timing experiment: The uncertainty in the time period of a vibrating body is found by dividing the least count of timing device by the number of vibrations. For example, the time of 30 vibrations of a simple pendulum recorded by a stopwatch accurate upto one tenth of a second is 54.6 s, the period
Thus, period T is quoted as T = 1.82 ± 0.003 s
Hence, it is advisable to count large number of swings to reduce timing uncertainty.
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Example 1.2: the mass of a metal box measured by a lever balance is 2.2kg. two silver coins of masses 10.01 g and 10.2 g measured by a beam balance are added to it. What is now the total mass of the box correct upto the appropriate precision.
Solution: total mass when silver coins are added to box
= 2.2 kg + 0.01001 kg + 0.01002 kg
Sine least precise is 202 kg, having one decimal place, hence total mass should be to one decimal place which is the appropriate precision. Thus the total mass = 202 kg.
The cesium atomic frequency standard at the national Institute of standards and technology in Colorado (USA), it is the primary standard for the unit of time.
Example 1.3: the diameter and length of a metal cylinder measured with the help of vernier calipers of least count 0.01 cm are 1.22 cm and 5.35 cm. calculate the volume V of the cylinder and uncertainty in it.
Solution: given data is
Diameter d = 1.22 cm with least count 0.01 cm
Length I = 5.35 cm with least count 0.01 cm
Absolute uncertainty in length = 0.01 cm
Absolute uncertainty in diameter = 0.01 cm
As volume is
total uncertainty in V = 2 ( %age uncertainty in diameter)
+ (%age uncertainty in length)
= 2 x 0.8 + 0.2 = 1.8%