28. 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.
SOLVED 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°
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View Full DocumentEx 2:
At what time between
2 and 3 o'clock
will the hands of a clock be together
?
Solution:
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 Spring '11
 vinh
 Hour, 3 days, 10 min, 60*5/55 min=60/11min

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