Clock

            Measurement of time is an important thing. It prepare us for a work in an orderly manner. This topic deals with clock and subsequently with time. There are mainly following important parts of a clock -

Dial, Hour - hand, Minute - hand and Second hand.

            The clock has 12 numbered from 1 to 12. Also, the clock is divided into 60 equal minute divisions. Therefore, each hour numbered, is separated by five minutes divisions.

60 Minute = An hour

30 Minute = Half an hour

15 Minute = Quarter of an hour

            The clock has a circular dial, which circumference is divided into 12 parts. Labeled as 1, 2, 3, 4, 5, .......... and 12. The space between every pair of two numbers is divided in 5 equal parts.

            Thus the clock's dial is divided into 60 small divisions. The clock has three hands. One is longest (Second hand), second is mid size (Minute hand) and smallest is (Hour hand).

            (1) Second hand - The longest hand of clock is known as second hand. The minute hand moves from one small division to the next small division in 1 second.

            The second hand goes once round the dial in 1 minute. Thus the second hand covers 60 small division in 1 minute.

60 Second = 1 Minute

            (2) Minute hand - The mid size clock's hand known as minute hand. The minute hand moves from one small division to the next small division in 1 minute.

            The minute hand goes once round the dial in 1 hour. Thus, the minute hand covers 60 small divisions in one hour.

60 minute = 1 Hour

            (3) Hour hand - The smallest hand of clock is known as hour hand. The hour hand moves from one number to the next number in one hour. The hour hand takes 12 h. to complete one round. Also, it takes 2 complete round of the clock in a day.

A day = 24 Hour

            It's movement is also in a clockwise direction.

AM and PM

            Time between 12 midnight and 12 noon is denoted by AM. Where AM stands for Ante - Meridian.

            Time between 12 noon and 12 midnight is denoted by PM, where PM stands for post - meridian. Thus, 4 PM refers to 4'O clock in the evening.

            We generally use 12 h clocks but Air lines, Railway time table, shipping lines, Television network etc. Do not use 12 h clock time. They use 24 h clock time. A 24 h clock dial may be visualised as the one given below.

            The first two digits on the left denote hours while the right two digit denoted minutes. The day starts at 12 midnight (12:00 AM) and is written as 00:00 h. Hence, the time in this clock type is expressed as 12 O'clock midnight is written as 2400 h or 0000 h.

            4:00 AM is written as 0400 h.

            10:00 AM is written as 1000 h.

            3:00 PM is written as 1500 h.

       If a watch or a clock indicates 9:15, when the correct time is 9, it is said to be 15 minutes too fast, on the other hand. It indicates 6:45, when the correct time is 6, it is said to be 15 minutes too slow and if it indicates 4:50 when the correct time is 5:00, it is said to be 10 minute slow.

  • One minute division = 360 over 60 = 6° apart, i.e., in one minute, the minute hand moves 6°
  • One hour division = 6° × 5 = 30° a part, i.e., in one hour, hand moves 30° apart.
  • Also, in one minute, the hour hand moves = fraction numerator 30 degree over denominator 60 degree end fraction equals fraction numerator 1 degree over denominator 2 end fraction apart.
  • Since, in one minute, minute hand moves 6° and hour hand moves fraction numerator 1 degree over denominator 2 end fraction, therefore, in one minute, the minute hand gains 5fraction numerator 1 degree over denominator 2 end fraction more than hour hand.
  • In one hour, the minute hand gains 5fraction numerator 1 degree over denominator 2 end fraction× 60 = 330° over the hour hand, i.e. the minute hand gains 55 minutes divisions over the hour hand.
  • In every hour, both the hand coincide once.
  • In a day, the hands are coinciding 22 times.
  • In every 12 hours, the hands of clock coincide 11 times.
  • In every 12 hour, the hands of clock are at right angles 22 times.
  • In every hour, the two hands are at right angles 2 times.
  • In every hour, the two hands are in opposite direction once.
  • In a day, the two hands are at right angles 44 times.
  • If the two hands coincide in time less than 65 5 over 11 minutes, then clock is too fast and if the two hands coincides in time more than 65 5 over 11 minutes, then the clock is too slow.
  • In 60 minute, the minute hand gain 55 minute on the hour hand.
  • In every hour, both the hands coincide once.
  • When the two hands are at right angles (90°) they are 15 minute space.
  • When the hands are in opposite direction, they are 30 minute space apart.
  • Angle traced by hour hand in 12 hour = 360°
  • Angle traced by minute hand in 60 minute = 360°
  • Both hands of a clock occurs right twice in one hour, 22 times in 12 h and 44 time in 24 h.

SOME IMPORTANT EXAMPLES —

1. The time in a clock is 20 minute past 2. Find the angle between the hands of the clock.

(A) 60 degrees                 (B) 120 degrees

(C) 50 degrees                 (D) 45 degrees

Answer – (D).  50 degrees

Solution : Time is 2:20. Position of the hands: Hour hand at 2 (nearly).

Minute hand at 4

Angle between 2 and 4 is 60 degrees [(360/12) × (4-2)]

Angle made by the hour hand in 20 minutes is 10 degrees, since it turns through ½ degrees in a minute.

Therefore, angle between the hands is 60 degrees - 10 degrees = 50 degrees

2. Calculate the angle between the two hands of clock when the clock shows 5 : 25 p.m.

(A) 12 degrees            (B) 12.5 degrees

(C) 15 degrees             (D) 20.5 degrees

Answer : (B)

Explanation : Since at 5 : 25 the minute hand will be at 5 and the angle between them will be same as the distance covered in degree by the hour hand in 25 minutes

Required angle = distance of hour hand = speed × time = 1/2 × 25 =12.5 degrees

3. How many non-leap years are there from 1801 to 1900?

(A) 74              (B) 75

(C) 77              (D) 76

Answer : (D)

Explanation : 100 years consists  24 leap years and 76 non-leap years (100th year is not a leap year if it cannot be divided  with 400)

4. If a light flashes every 6 seconds, how many times will it flash in ¾ of an hour?

(A) 451            (B) 450

(C) 350            (D) 425

Answer : (A)

Explanation : There are 60 minutes in an hour.

In ¾ of an hour there are (60 × ¾) minutes = 45 minutes.

In ¾ of an hour there are (60 × 45) seconds = 2700 seconds.

Light flashed for every 6 seconds.

In 2700 seconds 2700/6 = 450 times.

The count start after the first flash, the light will flashes 451 times in ¾ of an hour.

5.   Today is Monday. After 61 days, it will be:

(A) Wednesday                                                   (B) Saturday

(C) Tuesday                                                        (D) Thursday

Answer : (B)

Explanation : Each day of the week is repeated after 7 days.

So, after 63 days, it will be Monday.

After 61 days, it will be Saturday.

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