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Problem 2: The length of a pendulum is (1.5 ± 0.01) m and the acceleration due to gravity is taken (9.8 ± 0.1) ms-2. Calculate the time period of the pendulum with uncertainty in it.

Solution

Therefore, we should know about the calculation of uncertainty in the case of division and power.

  1. Quotient Rule:The percentage uncertainties in the numerator and denominator are added to find the percentage uncertainty in the quotient.

  2. Power Rule: We multiply the power with the percentage uncertainty of the base to find percentage uncertainty in power.

Now, given that, l = (1.5 ± 0.01) m and g = (9.8 ± 0.1) ms-2. So we find the percentage uncertainties of l and g.

Percentage uncertainty in length,

Percentage uncertainty in gravitational acceleration,

By division rule, add the percentage uncertainties in l and g to find the percentage uncertainty of l/g.

Percentage uncertainty in l/g = (0.67% + 1.02%) = 1.69% —– (C)

Now to find the percentage uncertainty in the term (l/g), use power rule and multiply the power (1/2) with the percentage uncertainty of l/g.

Percentage uncertainty in the whole term

Now to find the time period, apply the formula (1) above.

Therefore, time period along with percent uncertainty is given by,

3 Comments

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