Question

Suppose the length of a clock's pendulum is changed by 1.000%, exactly at noon one day. What time will it read 24 hours later, assuming it kept perfect time before the change? Note that there are two answers, and report your answers to the nearest second. Be sure to keep track of extra sig figs.

Answer 1

Period is given by

Case 1 :if length is shortened by 1 % i.e

L₂=(1-0.01)L₁ =0.99L₁

With shorter period ,the clock runs faster.Therefore clock reading is

In hour :minutes :seconds format

0.12090757*60 =7.2544542 minutes

0.2544542*60 =15.267252 seconds

Therefore  clock will display at noon i

P.M

Case 2 :if length is extended by 1 % i.e

L₂=(1+0.01)L₁ =1.01L₁

with longer period ,the clock runs slower

0.88089257*60 =52.8535539 minutes

0.8535539*60 =51.21323413 seconds

Therefore clock will read

A.M