The angular acceleration is maximum in case C
Explanation:
The motion of the bob in the simple pendulum is a portion of a circular motion. In a circular motion, the angular acceleration is related to the tangential acceleration by
where
a is the tangential acceleration
is the angular acceleration
r is the radius (the length of the pendulum)
Moreover for a pendulum, the tangential acceleration is given by the component of the acceleration of gravity in the tangential direction, so
where
g is the acceleration of gravity
is the angle of the pendulum with the vertical
So we have
Since g and r are constant, we see that the angular acceleration is proportional to the angle: the larger the angle, the larger the angular acceleration, and the smaller the angle, the smaller the angular acceleration.
Therefore, the angular acceleration is maximum when the pendulum is at its maximum height, and zero when it is at the lowest position. So, the correct statements are
It is maximum in case C
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