Question

A 321 g ball is tied to a string. It is pulled to an angle of 5.20 ∘ and released to swing as a pendulum. A student with a stopwatch finds that 16 oscillations take 16.5 s . How long is the string?

Answer 1

The Time Period is the time take for one oscillation. It is given as

  $T =2\pi {\sqrt \frac{l}{g}}$

l- Length of the Pendulum

g - Acceleration due to Gravity

From this formula we will calculate the length of the pendulum . Since the displacement is very small , we will ingrone the angle made by the pendulum. Also note that the period of the pendulum does not depend on the mass hanging at the end of the pendulum.

Given: Time taken by Oscillations 16.55 Time period T = 16.5 1.03s 16 Mass 3219 0.321 kg. TE 271 04 7²- 42 X aloo T² x 9 (1.03)2 x 9.8 412 4x(3.14) ² l= 10.39682 39 4364 li 02-636 m

Therefore the length of the string = 0.2636 m

Hope this Helps!!