Your grandfather clock's pendulum has a length of 0.9930 m. part a if the clock runs slow and loses 19 s per day, how should you adjust the length of the pendulum? note: due to the precise nature of this problem you must treat the constant g as unknown (that is, do not assume it is equal to exactly 9.80 m/s2).

Explanation:  

The period (T) of a simple pendulum depends on the length (l) of the pendulum and acceleration due to gravity (g). The period of a simple pendulum can be calculated as follows:

T= 2

The number of hours in a day is 24 h.

Convert 24 h to second as follows,

24 x 60 x 60 =86400  s

The number of cycle’s clock made per day is,

86400/2 = 43200

If the clock runs, slow of 19 s, then there is 9.5 cycles is reduces per day. So,

( 43200 -9.5) cycles  = 43190.5 cycles

The period would be reduces by.  43190.5/43200 = 0.9998

Then the new time period is,

T new = 0.9998 Told

Substitute

LNEW/LODD =

LNEW/LODD =0.9996

Substitute 0.9930 m for LODD

LNEW = 0.9930 X 0.9996 = 0.9926

The difference in the lengths is,

LNEW- LODD

= 0.9926-  0.9930 = -0.0004

This is the same as 0.4mm

Therefore, the new length of the pendulum is 0.9926m,  the length of the pendulum should be reduced by. 0.4mm