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Ex 5.2, 7 Where will the hour hand of a clock stop if it starts (a) from 6 and turns through 1 right angle? If it starts from 6 & turns 1 right angle, It will end up at 9 We know that 1 right angle = 1/4 of revolution = 1/4 × 12 hours = 3 hours
Answer
This implies it will stop at \[2\] on clock.
This implies it will stop at \[7\] on clock.
This implies it will stop at \[7\] on clock.
Note: Angle made by the hour hand in \[1\] hour is \[30\]. Angle made by the minute hand of a clock in \[1\] minute is \[6\]. Angle made by the second hand of the clock in \[1\] second is also\[6\]. The angle measured in the clock is always measured clockwise by default unless it is mentioned in any particular direction. However the angle measured in a clockwise direction is taken as a negative angle in trigonometry and slope concepts.
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We need to find where will the hour hand of a clock stop for the given set of questions Consider clock to be 360° and the clock marks up to 12 360/12 = 30 degrees per hour
(a) From 6 and turns through 1 right angle?
6 o’ clock = 6 X 30 = 180 °
From 180, a turn of right angle
180+90/ 30= 270/30= 9
So the hour hand would be at 9
(b) If the hour hand of a clock starts from 8 and turns through 2 right angle
8 o’clock = 8* 30° = 240°
240+2*90= 240+180= 420°
420/30= 14
We know that as per 24-hour format 14:oo hours stands for 2 o’clock
So, the hour hand would be at 2 o’clock
(c) If the hour hand of a clock starts from 10 and turns through 3 right angle
10 o’clock = 10* 30° = 300°
300+ 3*90 = 570/30 = 19
We know that as per 24-hour format 19:oo hours stands for 7 o’clock
So, the hour hand would be at 7 o’clock
(d) If the hour hand of a clock starts from 7 and turns through 2 straight angles, then it will stop at 7
7 o’ clock = 7* 30 = 210 °
210+ 2 * 180 = 210+360 = 570/30= 19
We know that as per 24-hour format 19:oo hours stands for 7 o’clock
So, the hour hand would be at 7 o’clock
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