-->

Mechanical Properties Of Fluids

Question
CBSEENPH11020249

A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be:

  • left parenthesis 92 space plus-or-minus 2 right parenthesis straight s
  • left parenthesis 92 space plus-or-minus 5 right parenthesis straight s
  • left parenthesis 92 space plus-or-minus space 1.8 right parenthesis straight s
  • left parenthesis 92 space plus-or-minus 3 right parenthesis straight s

Solution

A.

left parenthesis 92 space plus-or-minus 2 right parenthesis straight s

Arithmetic mean time of an oscillating simple pendulum
fraction numerator straight capital sigma space straight x subscript straight i over denominator straight N end fraction space equals space fraction numerator 90 space plus 91 space plus 92 space plus 95 over denominator 4 end fraction space equals space 92 space straight s
Mean deviation of a simple pendulum
equals fraction numerator straight capital sigma space vertical line space begin display style straight x with minus on top end style space minus space straight x subscript straight i vertical line over denominator straight N end fraction space equals space fraction numerator 2 space plus space 1 space plus 3 space plus space 3 space plus space 0 over denominator 4 end fraction space equals space 1.5
Given, minimum division in the measuring clock, i.e. simple pendulum = 1s. Thus, the reported mean time of an oscillating simple pendulum = left parenthesis space 92 space plus-or-minus space 2 right parenthesis straight s