Question

A 227 g ball is tied to a string. It is pulled to an angle of 9.62° and released to swing as a pendulum. A student with a stopwatch finds that 5 oscillations take 31 s. How long is the string?

Answer 1

9.55m

Step-by-step explanation:

From T = 2π√L/g ........ 1

Where T is the period

L is the length of the string and g is the acceleration due to gravity = 9.8m/s^2

Given that,

Mass of ball = 227g

The ball makes 5 oscillations in 31 s.

T = 31/5

T = 6.2s

Solving for L from equation 1

T = 2π√L/g

Square both sides

T^2 = 4π^2×L/g

T^2×g = 4π^2×L

Make L the subject

L = T^2*g/4π^2 ......... 2

Now, substitute the values into equation 2

L = 6.2^2 × 9.8/4×3.14^2

L = 38.44*9.8/39.4384

L = 376.712/39.4384

L = 9.55m

Hence, the length of the string is 9.55m