CBSE Class 11-science Answered
Figure shows a simple pendulum that has length and mass of bob is m.
If a small angular displacement θ is made as shown in figure , the torque τ on the bob is
.......................(1)
where g is acceleration due to gravity . Negative sign indicates the torque is in clockwise direction.
By Newton's second law , Torque τ acting on body is
........................(2)
where is moment of inertia and α is angular acceleration .
By equating (1) and (2) and after simplification, we get
........................ (3)
Above equation is equation of SHM , i.e. acceleration is proportional to displacement .
Negative sign indicates force is restoring force .
Proportionality constant in eqn.(3) is square of angular speed , i.e.,
Hence , we get
From above expression, we get period T of simple pendulum as