Q35 of 44 Page 9

Time for 20 oscillations of a pendulum is measured as t1= 39.6 s; t2= 39.9 s; t3= 39.5 s. What is the precision in the measurements? What is the accuracy of the measurement?

Given:


Time measurement for 20 oscillations of a pendulum


t1=39.6s


t2=39.9s


t3=39.5s


Since, all the measurements have a maximum of on decimal place, the lease count of the instrument used to measure the time is 0.1s.


Since precision in measurement is equal to the least count of the instrument, therefore




Now the mean value of time period of the pendulum for 20 oscillations:




Now mean time period for one oscillation:



Now accounting for the precision in measuring time for one oscillation we have the measured mean time period



Now the accuracy in measurement is given by the maximum observed error from the measured value, which is



More from this chapter

All 44 →
33

Calculate the solid angle subtended by the periphery of an area of 1cm2 at a point situated symmetrically at a distance of 5 cm from the area.

 34

The displacement of a progressive wave is represented by y = A sin(wt – k x ), where x is distance and t is time. Write the dimensional formula of (i) ω and (ii) k.

 36

A new system of units is proposed in which unit of mass is α kg, unit of length β m and unit of time γ s. How much will 5 J measure in this new system?

 37

The volume of a liquid flowing out per second of a pipe of length l and radius r is written by a student as


where P is the pressure difference between the two ends of the pipe and η is coefficient of viscosity of the liquid having dimensional formula ML-1 T-1. Check whether the equation is dimensionally correct.