Numerical Problem 2, Measurement … msa

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.

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

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,