If the length of seconds pendulum is decreased by 1%, the gain or lose time per day by the pendulum will be

Options

A. gain 432 s
B. lose 443 s
C. gain 4.4 s
D. lose 0.44 s

Answer

A

Explanation

`l_(2)=(l_(1)-0.01)`
`T_(1)=2pisqrt((l)/(g))andT_(2)=2pisqrt((0.99)/(g))`
`(T_(2))/(T_(1))=sqrt((0.99)/(1))`
`therefore T_(2)=2sqrt(99xx10^(-2))=2xx9.95xx10^(-1)`
`T_(2)=1.990s`
In 1 osci. Gain of time is, `2-1.990=0.01` s
`therefore` In one day i.e. 43200 oscillations
The time gain is 43200 `xx` 0.01 = 432