Question

A 163 g ball is tied to a string. It is pulled to an angle of 7.8 ∘and released to swing as a pendulum. A student with a stopwatch finds that 30 oscillations take 17 s .

How long is the string?

Answer 1

given mass of ball, m = 0.163 g
intitial angle, thetao = 7.8 deg
for n = 30 osscilations, t = 17 s
hence

time period T = t/n = 17/30 s
now
for a pendulum
T = 2*pi*sqrt(l/g)
hence

17/30 = 2*pi*sqrt(l/9.81)
l = 0.079792965 m = 7.9792965147932053456341174264241 cm