Question

A 200 g ball is tied to a string. It is pulled to an angle of 8.0° and released to swing as a pendulum. A student with a stopwatch finds that 10 oscillations take 12 s. How long is the string?

Answer 1

The string is 36 cm long.

Explanation:

Period of simple is given by the equation

              $T=2\pi\sqrt{\frac{l}{g}}$

It will not depend upon angle and mass of ball.

A student with a stopwatch finds that 10 oscillations take 12 s.

So we can find period for 1 oscillation

                   $\texttt{Period, T = }\frac{12}{10}=1.2s$

Substituting in equation of period

                    $T=2\pi\sqrt{\frac{l}{g}}\\\\1.2=2\pi\sqrt{\frac{l}{9.81}}\\\\l=\frac{1.2^2\times 9.81}{4\pi^2}\\\\l=0.36m$

The string is 0.36 m long.

The string is 36 cm long.