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

timing_experiment-equation_1

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.

For your information

Moon to earth        1 min 20sSun to earth            8 min 20sPluto to earth          5 h 20s

 

Example 1.1:the length, breadth and thickness of a sheet are 3.233m, 2.105 m and 1.05 m respectively. Calculate the volume of the sheet correct upto the appropriate significant digits.Solution: given length i= 3.233 mBreadth b = 2.105mgiven_length-equation
As the factor 1.05 cm has minimum number of significant figures equal to three, therefore, volume is recorded upto 3 significant figures, hence, hence_equation

 

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

=2022003 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.

 

 Atomic_Clock

Atomic Clock

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

age_uncertainty_length_equation

Absolute uncertainty in diameter = 0.01 cm

diameter_equation

As volume is            volume_equation

 total uncertainty in V = 2 ( %age uncertainty in diameter)

+ (%age uncertainty in length)

= 2 x 0.8 + 0.2 = 1.8%

equation-01

1.8% uncertainty

calculated_volume_equation

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