Introduction
A clock is an instrument to indicate, keep, and co-ordinate time. The word clock is derived ultimately (via Dutch, Northern French, and Medieval Latin) from the Celtic words clagan and clocca meaning "bell".clock, instrument for measuring and indicating time. Predecessors of the clock were the sundial, the hourglass, and the clepsydra.
Formulae & Examples
Formula for finding out Clock.
1. Minute Spaces:
The face or dial of watch is a circle whose circumference is divided into 60 equal parts, called minute spaces.
2. Hour Hand and Minute Hand:A clock has two hands, the smaller one is called the hour hand or short hand while the larger one is called minute hand or long hand.
3. i)In 60 minutes, the minute hand gains 55 minutes on the hour 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 hands 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°.
viii)If a watch or a clock indicates 8.15, when the correct time is 8, it 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.
4. The hands of a clock will be in straight line but opposite in direction, 22 times in a day
5. The hands of a clock coincide 22 times in a day
6. The hands of a clock are straight 44 times in a day
7. The hands of a clock are at right angles 44 times in a day
8. The two hands of a clock will be together between H and (H+1) o' clock at (60H11)minutes past H o' clock.
9. The hands of a clock are at right angles 44 times in a day
10. Angle between Hands of a clockWhen the minute hand is behind the hour hand, the anglebetween the two hands at M minutes past H'o clock=30(H−M5)+M2 degreeWhen the minute hand is ahead of the hour hand, the anglebetween the two hands at M minutes past H'o clock=30(M5−H)−M2 degree
11. The two hands of the clock will be at right angles between H and (H + 1) o' clock at(5H±15)1211minutes past H 'o clock
12. The minute hand of a clock overtakes the hour hand at intervalsof M minutes of correct time. The clock gains or loses in a day by=(72011−M)(60×24M) minutes
13. Bbetween H and (H + 1) o' clock, the two hands of a clock are M minutes apart at(5H±M)1211minutes past H 'o clock
Sample Example
Ex
Find at what time between 9 and 10 o'clock will the hands of a clock be in the same straight line but not together ?
A
At 9 o'clock hour hand 15 min space apart from minute hand.
Also minute hand has gain of (30-15)= 15 min spaces apart over hour hand
For both hand to be straight but not together they will be 30 min space apart.
55 min space gained by min hand in 60 min
So, 15 min spaces will be gined in =((60/55)*15)min = (16*(4/11))min
Ex
At what time between 8 and 9 o'clock will the hands of a clock be at right angle ?
A
At 8 o'clock min hands are 20 min space ahead the hour hand.
Also when both hands are at right angled, they are 15 mins space apart.
Case 1: when min hand 15 min space ahead the hour hand
In this case min hand has a gain of (20-15)= 5 min
now 55 min space is gained in 60 min
So, 5 min space will be gined in = ((60/55)5)min = (5(5/11))min
So both hands will be at right angled at 5(5/11)min.
Case 2: When min hand 15 space behind the hour hand
In this case min. hand has a gain of (20+15) = 35 min
now 55 min space is gained in 60 min
So, 35 space is gained by min hand in = ((60/55)35) = (38(2/11))min
So both hands will be at right angled at 38(2/11)min.
Ex
A clock is set right at 8 a.m. The clock loses 1 minutes in 24 hours. What will be true time when clock indicates 8 p.m on the third day ?
A
Time from 8 a.m. on first day to 8 p.m of third day = 60 hrs
also 23 hrs and 45 min = 95 / 4 hrs
95/4 hrs of this clock = 24 hrs of correct clock
So 60 hrs of this clock = (24*(4/95)*60)=60(96/95)= 61 hrs approx
= 61 hrs of correct clock, So, the correct time will be 9 p.m