If the length of a correct pendulum clock is raised by `0.1%`, what will be the effect on the time of the clock in a day ?

Options

A. Time loss per day is `43.2s`
B. Time loss per day is `86.4 s`
C. Time gain per day is `43.2 s`
D. Time gain per day is 86.4 s`

Answer

A

Explanation

Correct time for pendulum clock `=2s`
If `L` is the length of correct second pendulum, then
`s=2pisqrt((L)/(g))`
If length of pendulum increases by `0.1%`, the new length is
`L^(')=L+(0.1)/(100)L=L+(L)/(1000)=L(1+(1)/(1000))`
Now, time period, `T^(')=2pi(sqrt(L(1+(1)/(1000))))/(g)`
`:. (T^('))/(2)=(1+(1)/(1000))^(2)=(1+(1)/(2)xx(1)/(1000)+....)`
or`T^(')=2+(1)/(1000)s`
Time loss in 2 seconds `=(1)/(100)s`
Total time loss in 1 day `(=24xx60xx60s)`
`=(1)/(1000)xx(24xx60xx60)/(2)=43.2s`