Where will the hour hand of a clock stop if it starts from 7 and turns through two straight angles

Last updated at Nov. 12, 2021 by

Introducing your new favourite teacher - Teachoo Black, at only ₹83 per month

Ex 5.2, 7 Where will the hour hand of a clock stop if it starts (d) from 7 and turns through 2 straight angles? We know that 1 straight angle = 1/2 of revolution = 1/2 × 12 hours = 6 hours We start from 7, and move 1 straight angle (12 hours) to 1 We start from 7, and move 1 straight angle (12 hours) to 1

Where will the hour hand of a clock stop if it starts: a From 6 and turns through 1 right angle? b From 8 and turns through 2 right angles? c From 10 and turns through 3 right angles? d From 7 and turns through 2 straight angles?

Suggest Corrections

Answer

Verified

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.