Question

1. where will the hour hand of a clock stop if it starts

(a) from 4 and turns through 2 right angle?
(b) from 8 and turns through 1 right angles?
(c) from 1 and turns through 5 right angles?
(d) from 5 and turns through 3 straight angles?
ans. (a)
(b)
(c)
(d)

Explanation:

Step1: Calculate the number of hours per right - angle

A right - angle on a clock is \(3\) hours (since a full circle of the clock is \(12\) hours and \(360^{\circ}\), and \(90^{\circ}\) corresponds to \(\frac{12}{4}=3\) hours). A straight - angle on a clock is \(6\) hours (since \(180^{\circ}\) corresponds to \(\frac{12}{2} = 6\) hours).

Step2: Solve part (a)

Starting from \(4\), if it turns through \(2\) right - angles. Each right - angle is \(3\) hours. So the number of hours moved is \(2\times3=6\) hours. \(4 + 6=10\).

Step3: Solve part (b)

Starting from \(8\), if it turns through \(1\) right - angle. Each right - angle is \(3\) hours. So \(8+3 = 11\).

Step4: Solve part (c)

Starting from \(1\), if it turns through \(5\) right - angles. Each right - angle is \(3\) hours. The number of hours moved is \(5\times3 = 15\) hours. \(1+15=16\). Since \(16-12 = 4\) (because the clock has a \(12\) - hour cycle).

Step5: Solve part (d)

Starting from \(5\), if it turns through \(3\) straight - angles. Each straight - angle is \(6\) hours. The number of hours moved is \(3\times6=18\) hours. \(5 + 18=23\). Since \(23-12=11\) (because of the \(12\) - hour cycle of the clock).

Answer:

(a) \(10\)
(b) \(11\)
(c) \(4\)
(d) \(11\)