Where will the hour hand of a clock stop if it starts from 9 and turns through 2 right angles

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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

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

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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Answer

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b) Hour hand of clock stops when it starts from \[8\] and turns \[2\] right angles:Again here we have \[2\] right angles, one right angle measures \[3\] hours. So \[2\] right angles will count for \[3 \times 2 = 6{\text{ }}hours\]Hence the clock hand will stop at \[8 + 6 = 14hours\]As the clock is of \[12\] hours marks only so \[14 - 12 = 2\]

This implies it will stop at \[2\] on clock.

c) Hour hand of clock stops when it starts from\[10\] and turns \[3\] right angles:Here we have \[3\] right angles, as one right angle measure for \[3\] hours so \[3\] right angles will count \[3 \times 3 = 9{\text{ }}hours\]Hence the clock will stop at \[10 + 9 = 19{\text{ }}hours\]As the clock is of \[12\] hours marks only so \[19 - 12 = 7\]

This implies it will stop at \[7\] on clock.

d) Hour hand of clock stops when it starts from \[7\] and turns \[2\] straight angles:Here we have \[2\] straight angles. One straight angle measure \[6\] hours here we have\[2\] straight angles so it counts for \[6 \times 2 = 12{\text{ }}hours\]Hence the clock will stop at \[7 + 12 = 19{\text{ }}hours\]As the clock is of \[12\] hours marks only so \[19 - 12 = 7\]

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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