Question

An accepted value for the acceleration due to gravity is 9.801 m/s2. In an experiment with pendulums, you calculate that the value is 9.4 m/s2. Should the accepted value be tossed out to accommodate your new finding? Explain.

Answer 1

g Generally the accepted value of acceleration due to gravity is 9.801 $m/s^2$

as per the question the acceleration due to gravity is found to be 9.42$m/s^2$ in an experiment performed.

the difference between the ideal and observed value is 0.381.

hence the error is -$\frac{0.381}{9.801} *100$

                                                            =3.88735 percent

the error is not so high,so it can be  accepted.

now we have to know why this occurs-the equation of time period of the simple pendulum is give as-$T=2\pi\sqrt[2]{l/g}$

                                                      $g=4\pi^2\frac{l}{T^2}$

As the experiment is done under air resistance,so it will affect to the time period.hence the time period will be more which in turn decreases the value of g.

if this experiment is done in a environment of zero air resistance,we will get the value of g which must be approximately equal to 9.801  $m/s^2$