Question

The length of a pendulum is 70 cm and it describes an arc of length 88 cm when swings. The angle subtended by the arc at the centre is

• A. \(36^\circ\)
• B. \(70^\circ\)
• C. \(72^\circ\)
• D. \(80^\circ\)

Hint:

To make calculations fast and error-free: Always simplify the numbers before multiplying them out fully.
Cancelling the common factor of 10 from 360 and 440 first makes the calculation extremely simple: \(\theta = \frac{88 \times 36}{44} = 2 \times 36 = 72^\circ\).

Answer 1

The Correct Option is C

Step 1: Identify given values.
Radius (length of pendulum) \(r = 70\) cm, arc length \(l = 88\) cm. We need to find the central angle \(\theta\).
Step 2: Recall the arc length formula.
\(l = \frac{\theta}{360^\circ} \times 2\pi r\), where \(\theta\) is in degrees.
Step 3: Substitute the values.
\(88 = \frac{\theta}{360} \times 2 \times \frac{22}{7} \times 70\).
Step 4: Simplify the right side.
\(2 \times \frac{22}{7} \times 70 = 2 \times 22 \times 10 = 440\). So \(88 = \frac{\theta}{360} \times 440\).
Step 5: Solve for \(\theta\).
\(\theta = \frac{88 \times 360}{440} = \frac{31680}{440} = 72^\circ\).
Step 6: Select the correct option.
The angle subtended is \(72^\circ\), which is option 3.
\[ \boxed{72^\circ} \]