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 :

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°
(C) 72°
(B) 70°
(D) 80°

Solution : Correct answer is : (B) 70°

Length of pendulum = 70 cm
(This is the radius of the circular arc.)

Arc length = 88 cm

Recall the arc length formula

$$\text{Arc length} = r\theta$$Here, θ must be in radians.

Substitute values

$$88 = 70 \times \theta$$$$\theta = \frac{88}{70}$$$$\theta = 1.257 \text{ radians}$$Convert radians to degrees

We know:$$1 \text{ radian} = \frac{180}{\pi}^\circ$$

So,$$\theta = 1.257 \times \frac{180}{\pi}$$

Taking π ≈ 3.14:$$\theta = 1.257 \times 57.3$$$$\theta \approx 72^\circ$$

Final Answer:

$$\boxed{72^\circ}$$

Correct answer is : (B) 70°