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The time taken by a simple pendulum to p...

The time taken by a simple pendulum to perform 100 vibration is 8 minutes 9 sec in bombay and 8 minutes 20 sec. in pune. Calcualte the ratio of acceleration due to gravity in bombay and pune.

Text Solution

Verified by Experts

The correct Answer is:
`1.05`
Let ` g_(1) and g_(2)` be the values of acceleration due to gravity in Mumabi and Pune and ` T_(1) and T_(2)` be the values of the time periods at the respective places
Then ,
`T_(1) = (8 "min" 9 s)/( 100) = (489)/(100) s = 4.89 s`
`T_(2) = (8 "min"20 s) /(100) = (500 s)/( 100) = 5 s`
As ` (T_(2))/( T_(1)) = sqrt((g_(1))/(g_(2)))`
`:. (g_(1))/(g_(2)) = (T_(2)^(2))/(T_(1)^(2)) = ((5)^(2))/((4.89)^(2)) ~~1.04`
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