Mathematics
Where will the hour hand of a clock stop if it
(i) starts at 10 and makes of a revolution, clockwise?
(ii) starts at 4 and makes of a revolution, clockwise?
(iii) starts at 4 and makes of a revolution, clockwise?
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Answer
One complete revolution of the hour hand = 12 hours.
(i) of a revolution = = 6 hours
Starting from 10 and moving 6 hours clockwise: 10 → 11 → 12 → 1 → 2 → 3 → 4
∴ The hour hand will stop at 4.
(ii) of a revolution = = 3 hours
Starting from 4 and moving 3 hours clockwise: 4 → 5 → 6 → 7
∴ The hour hand will stop at 7.
(iii) of a revolution = = 9 hours
Starting from 4 and moving 9 hours clockwise: 4 → 5 → 6 → 7 → 8 → 9 → 10 → 11 → 12 → 1
∴ The hour hand will stop at 1.
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Related Questions
In the adjoining figure, measure the lengths of the sides of the triangle ABC and verify:
(i) AB + BC > AC
(ii) BC + AC > AB
(iii) AC + AB > BC
What fraction of a clockwise revolution does the hour hand of a clock turn through when it goes from:
(i) 4 to 10
(ii) 2 to 5
(iii) 7 to 10
(iv) 8 to 5
(v) 11 to 5
(vi) 6 to 3
Also find the number of right angles turned in each case.
Where will the hour hand of a clock stop if it starts from
(i) 6 and turns through 1 right angle?
(ii) 8 and turns through 2 right angles?
(iii) 10 and turns through 3 right angles?
(iv) 7 and turns through 2 straight angles?
What fraction of a revolution have you turned through if you stand facing
(i) north and turn clockwise to face west?
(ii) south and turn anti-clockwise to face east?
(iii) east and turn clockwise (or anti-clockwise) to face west?
Also find the number of right angles turned in each case.