Question

A 10.67-cm-long, 216 g rod is pivoted at one end. A 19 g ball of clay is stuck on the other end. What is the period if the rod and clay swing as a pendulum?

Answer 1

Given that

The length of the rod (L) = 10.67cm

                                      = 0.1067m

The mass of the rod (M) = 0.216kg

The mass of the clay (m) = 19g

                                     = 0.019kg

Accceleration due to gravity (g) =9.8m/s²

We know that the time period of the rod and clay using as apendulum

                          T = 2π√I/mgh

Now the moment of inertia is given by

                          I = (1/3)ML² +mL²

The height reached by the rod and clay swing is given by

                         h = x_cm = mx₁ + Mx₂/ (m+M)

Here the distnace (x₁) =L = 0.1067m and x₂ = (L/2)= 0.05335m

Now substitute all the above values to get the requiredanswer