Question

A pendulum swings through an angle 60 degree and describes an arc 8.8cm in length. Find the length of pendulum.

Answer 1

we know that formula for the length of arc =theeta/360*2pie* r

so

60 /360*2*22/7*r=8.8
2.096r=8.8
r = 4.271 on simplification:
so length of pendulum is 4.271 cm.

Answer 2

Answer:

Length of the pendulum = 8.4cm

Step-by-step explanation:

Given,

A pendulum swings through an angle of 60 degree and describes an arc 8.8cm in length

To find,

The length of the pendulum

Solution:

Recall the formula,

Arc length =$\frac{\theta}{360} 2\pi r$$\frac{60}{360} 2\pi r$, where θ, is the angle subtended at the center and r is the radius of the circle

If we take the point of suspension of the pendulum as the center of the circle and the length of the pendulum as the radius of the circle.

Then by the given condition, we have,

The arc of length 8.8cm subtends an angle of 60° at the center.

We know,

Arc length =  $\frac{\theta}{360} 2\pi r$

Here θ = 60° and Arc length = 8.8cm

and r is the length of the pendulum

Substituting these values we get,

8.8 = $\frac{60}{360} 2\pi r$

8.8 =$\frac{1}{6} X2X\frac{22}{7} Xr$

8.8 = $\frac{22}{21} r$

r = $\frac{8.8X21}{22}$ =8.4cm

r =  8.4cm

Length of the pendulum = 8.4cm

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