Clocks

CLOCKS

 

IMPORTANT FACTS

The Face or dial of a watch is a circle whose circumference is divided into 60 equal parts, called minute spaces. A clock has two hands, the smaller one is called the hour hand or short hand while the larger one is called the minute hand or long hand..

i)  In 60 minutes, the minute hand gains 55 minutes on the hour hand.

ii) In every hour, both the hands coincide once.

iii) The hands are in the same straight line when they are coincident or opposite to each other.

iv) When the two hands are at right angles, they are 15 minute spaces apart.

v)When the hand's are in opposite directions, they are 30 minute spaces apart.

vi)Angle traced by hour hand in 12 hrs = 360°.

vii)Angle traced by minute hand in 60 min. = 360°.    

Too Fast and Too Slow: If a watch or a clock indicates 8.15, when the correct time , 8 is said to be 15 minutes too fast. On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow.

 

Examples:

Ex 1:Find the angle between the hour hand and the minute hand of a clock when 3.25.

Solution:angle traced by the hour hand in 12 hours = 360°

Angle traced by it in three hours 25 min (ie) 41/12 hrs=(360*41/12*12)° =102*1/2°

angle traced by minute hand in 60 min. = 360°.

Angle traced by it in 25 min. = (360 X 25 )/60= 150°

Required angle = 1500 – 102*1/2°= 47*1/2°

Ex 2:At what time between 2 and 3 o'clock will the hands of a clock be together?

Solution: At 2 o'clock, the hour hand is at 2 and the minute hand is at 12, i.e. they are 10 min spaces apart.

To be together, the minute hand must gain 10 minutes over the hour hand.

Now, 55 minutes are gained by it in 60 min.

10 minutes will be gained in (60 x 10)/55 min. = 120/11 min.

The hands will coincide at 120/11 min. past 2.

   

Ex. 3. At what time between 4 and 5 o'clock will the hands of a clock be at right angle?

Sol: At 4 o'clock, the minute hand will be 20 min. spaces behind the hour hand, Now, when the two hands are at right angles, they are 15 min. spaces apart. So, they are at right angles in following two cases.

Case I. When minute hand is 15 min. spaces behind the hour hand:

In this case min. hand will have to gain (20 - 15) = 5 minute spaces. 55 min. spaces are gained by it in 60 min.

5 min spaces will be gained by it in 60*5/55 min=60/11min.

:. They are at right angles at 60/11min. past 4.

Case II. When the minute hand is 15 min. spaces ahead of the hour hand:

To be in this position, the minute hand will have to gain (20 + 15) = 35 minute spa' 55 min. spaces are gained in 60 min.

35 min spaces are gained in (60 x 35)/55 min =40/11

:. They are at right angles at 40/11min. past 4