1.

How can the depth of well is measured and also estimate the % of real error .

Answer»

SOLUTION :(i) Consider a well without water, of some depth d . Take a small object ( for example lemon ) and a stopwatch . When you drop the lemon, start the stop watch . As SOON as the lemon touches the bottom of the well , stop the watch . Note the time taken by the lemon to reach the bottom and denote the time as t.
(ii) Since the INITIAL velocity of lemon `u = 0` and the ACCELERATION due to gravity g is constant over the well, by using use the equations of motion for constant acceleration.
`s=ut+(1)/(2)at^(2)`
(iii) `u=0, s=d, a=g` (Since we choose the y axis downwards), Then
`d=(1)/(2)g t^(2)`
(iv) Substituting`g = 9.8 ms^(-2)`the depth of the well is obtained .
(v) To estimate the error in calculation another method is used to measure the depth of the well .
(vi) Take a long rope and hang the rope inside the well TILL it touches the bottom . Measure the length of the rope which is the correct depth of the well `(d_("correct") )`. Then
`"error"=d_("correct")-d`
`"relative error"=(d_("correct")-d)/(d)`
percentage of relative error
`=(d_("correct")-d)/(d_("correct"))xx100`


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