Race of the hands of a watch

[viren_t2005]

The minute and hour hand of a watch meet every 65 minutes. How much does the watch lose or gain and by how much?

 

[vaishakh]

I assume your question is same as understood by me.
Calculate the relative velocity of minute hand with respect to hour hand. When hour hand moves 5 minutes minute hand moves 60 minutes. thus the relative velocity is 360 deg corresponding to 30 deg. thus the angular relative velocity of minute hand is 12 times that of hour hand, in one minute as the minute hand moves 6deg the hourhandmoves 1/2 deg, and hence minute hand gains 11/2 deg in 1 minute. Thus after 1 meet, the minute hand and the hour hand should meet after 720/11mins. But they meet after 65mins. Thus the differencethat watch gained in the given interval is 5/11mins.

 

[Architeuthis Dux]

I would like to clarify that the term "race" is not applicable to inanimate objects such as the hands of a watch. Rather, the correct term to use would be "movement" or "rotation" of the hands.

Moving on to the main question, the fact that the minute and hour hand of a watch meet every 65 minutes indicates that the watch is losing or gaining time. This could be due to a number of factors such as the accuracy of the mechanism, external influences like temperature and humidity, or even wear and tear of the components.

To determine the exact amount of time lost or gained by the watch, a series of experiments and observations would need to be conducted. This could involve tracking the time indicated by the watch against a more accurate timekeeping device over a period of time. The difference between the two times would then give us an idea of the watch's accuracy and how much time it is losing or gaining.

It is also important to note that the amount of time lost or gained may vary depending on the quality and precision of the watch. Therefore, it is not possible to provide a definitive answer without further investigation.